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50 CT15 Abstracts
IP1
Stochastic Target Problems
In these class of optimization problems, the controller triesto steer the state process into a prescribed target set withcertainty. The state is assumed to follow stochastic dynam-ics while the target is deterministic and this miss-matchrenders the problem difficult. One exploits the degenera-cies and/or the correlations of the noise process to deter-mine the initial positions from which this goal is feasible.These problems appear naturally in several applications inquantitative finance providing robust hedging strategies.As a convenient solution technique, we use the geometricdynamic programming principle that we will describe inthis talk. Then, this characterization of the reachabilitysets will be discussed in several examples.
Halil Mete SonerETH [email protected]
IP2
A Convex Optimization Approach to Infinite-Dimensional Systems
Time-delay appears naturally in many control systems. Itis frequently a source of instability although, in some sys-tems, it may have a stabilizing effect. A time-delay ap-proach to sampled-data control, which models the closed-loop system as continuous-time with delayed input/output,has become popular in the networked control systems(where the plant and the controller exchange data via com-munication network). Many important plants (e.g. flexiblemanipulators and heat transfer processes) are governed byPDEs and are described by uncertain nonlinear models. Inthis talk Lyapunov-based methods for time-delay and dis-tributed parameter systems leading to finite-dimensionalLinear Matrix Inequalities (LMIs) will be presented. TheLMI approach provides an effective and simple tool for ro-bust control of uncertain infinite-dimensional systems.
Emilia FridmanTel Aviv University, [email protected]
IP3
Simple Distributed Control of Networked Systems:Learning, Direct and Indirect Communications
We consider collaborative decision making and control inmulti-agent systems. The emphasis is to derive simple dis-tributed algorithms that work provably very well, whilehaving minimal knowledge of the system and its parame-ters; thus the need for learning. We consider a behaviorlearning algorithm for a class of behavior functions andstudy its effects on the emergence of agent collaboration.Next we consider systems, with each agent picking actionsfrom a finite set and receiving a payoff depending on theactions of all agents. The exact form of the payoffs is un-known and only their values can be measured by the re-spective agents. We develop a decentralized algorithm thatleads to the agents picking welfare optimizing actions uti-lizing the impact of agents actions on their payoffs, and ifneeded very simple bit-valued information exchanges be-tween the agents. We next consider the continuous timeand continuous state space version of the problem basedon ideas from extremum seeking control. Our results showhow indirect communications (signaling between the agentsvia their interactions through the system) and direct com-
munications (direct messages sent between the agents) cancomplement each other and lead to simple distributed con-trol algorithms with remarkably good performance. Weclose by discussing the role of communication and influ-ence connectivities and the need for new non-commutativeprobability models to model and analyze humans in suchnetworked systems.
John BarasUniv. MarylandCollege [email protected]
IP4
Irreversibility in Dynamic Optimization
Irreversibility is the property that characterizes evolution-ary processes which do not allow for time inversion. InDynamic Optimization, such a behavior is expected fornoise-perturbed systems but it also takes place in the de-terministic case: being able to solve the Hamilton-Jacobiequation forward in time from some initial data and thenbackward, resulting in the same data, often implies the so-lution is smooth. Analyzing these phenomena may helpto exploit optimization techniques in their full strength.This talk will discuss irreversibility effects such as the gainof regularity of solutions, the loss of regularity due to theonset and persistance of singularities, and compactness es-timates for the flow.
Piermarco CannarsaUniversity of Rome ”Tor Vergata”, [email protected]
IP5
Hybrid Processes for Controlling ManufacturingSystems
Revolutionary computing technologies are driving signifi-cant advances in the manufacturing domain. High-fidelitysimulations and virtual design environments allow unprece-dented opportunities to test and validate systems beforethey are built, reducing overall design time and cost. Tor-rents of data streaming from the factory floor can be col-lected over high-speed networks, and stored in large-scaleserver farms (such as cloud-based systems), enabling im-proved analytics and increased performance. This talk willdescribe how the integration of simulation and plant-floordata can enable new control approaches that are able tooptimize the overall performance of manufacturing systemoperations.
Dawn TilburyUniversity of Michigan, [email protected]
IP6
Averaged Control
This lecture is devoted to address the problem of control-ling uncertain systems submitted to parametrized pertur-bations. We introduce the notion of averaged control ac-cording to which the average of the states with respectto the uncertainty parameter is the quantity of interest.We observe that this property is equivalent to a suitableaveraged observability one, according to which the initialdatum of the uncertain dynamics is to be determined bymeans of averages of the observations done. We will firstdiscuss this property in the context of finite-dimensional
CT15 Abstracts 51
systems to later consider Partial Differential Equations,mainly, of wave and parabolic nature. This analysis willlead to unexpected results on the robustness of observabil-ity estimates with respect to additive perturbations. Weshall also highlight that the averaging process with respectto the unknown parameter may lead a change of type on thePDE under consideration from hyperbolic to parabolic, forinstance, significantly affecting the expected control theo-retical properties. We shall link these results to well-knownphenomena on regularisation by averaging. We will alsopresent some open problems and perspectives of future de-velopments. This work has been developed in collaborationwith J. Lohac, M. Lazar and Q. Lu.
Enrique ZuazuaIkerbasque & Basque Center for Applied Mathematics([email protected]
SP1
W.T. and Idalia Reid Prize in Mathematics Lec-ture: Definitions and Hypotheses and All ThatStuff
There are times when a satisfactory analysis of a problemin control requires certain abstract tools which may ap-pear somewhat esoteric at first. In this non technical talk,we illustrate this proposition with some examples in whichlack of existence, non smooth behavior, and discontinuousfeedback are involved.
Francis ClarkeUniversite Claude Bernard Lyon 1, [email protected]
SP2
SIAG/CST Prize Lecture - Control of Higher Or-der PDEs: KdV and KS Equations
Higher-order PDEs appear to model different nonlinearpropagation phenomena. This class of equations in-cludes the Korteweg-de Vries (KdV) and the Kuramoto-Sivahinsky (KS) equations. The first one is dispersive whilethe second one is parabolic. In despite of this great differ-ence, they have in common some important features. Forinstance, both of them present critical spatial domains forwhich the boundary controllability does not hold. In thistalk we aim at explaining the main results and methodsconcerning the control and stabilization of these nonlinearone-dimensional PDEs.
Eduardo CerpaUTDSM - Universidad Tecnica Federico Santa [email protected]
CP1
Approximate Controllability of Second OrderSemilinear Stochastic System with Variable Delayin Control and with Nonlocal Conditions
This paper deals with the approximate controllability ofsecond Order semilinear stochastic system with variabledelay in control and with nonlocal conditions. The resultis obtained by using Banach fixed point theorem. At theend, an example is given to show the effectiveness of theresult.
Urvashi AroraIIT Roorkee
N. SukavanamIIT Roorkee, [email protected]
CP1
Controlled Invariance and Dynamic Feedback forSystems over Semirings
The concept of (A,B)-invariant subspace is the fundamen-tal concept of the geometric approach of control design.It has been extended by many authors to that of (A,B)-invariant module or semimodule, for the sake of extendingthe solution of various control problems to the case of sys-tems over rings or semi rings. In this paper is discussedthe use of dynamic feedback control laws for systems oversemirings, and it is shown that an (A,B)-invariant semi-module over a commutative semiring can be made invariantfor the closed-loop system by dynamic feedback.
Jean Jacques Loiseau, Carolina Cardenas, ClaudeMartinezIRCCyN Nantes, [email protected], [email protected], [email protected]
CP1
Normal Forms of Linear Multivariable Square Sys-tems and Their Application
Normal forms called by Byrnes-Isidori are useful to studyproperties of zeros of controlled systems in continuous-timeand sampled-data domain for the design of feedback con-trollers. This paper investigates how transfer function ma-trices and state-space equations of linear square systemsare transformed to normal forms, and applies the resultsto analysis of zeros of sampled-data models correspondingto continuous-time linear square systems nondecouplableby static state feedback.
Mitsuaki Ishitobi, Sadaaki KunimatsuKumamoto [email protected], [email protected]
CP1
Differential Controllability and Observability Func-tions with Applications to Model Reduction
In this talk, we aim at constructing a nonlinear balancingmethod in the contraction framework. We introduce thenotion of differnetial controllability and observability func-tions, and we provide characterizations for them. Then,we define the differential balanced realization and studymodel reduction for such a realization.
Yu KawanoKyoto [email protected]
Jacquelien M. ScherpenRijksuniversiteit Groningen
52 CT15 Abstracts
CP1
Relative Controllabilty Properties
For nonlinear systems described by ordinary differentialequations, we present the notion of W -control sets whichare defined as maximal subsets of complete approximatecontrollability within a safe region or world W in the statespace. In articular, their relative invariance properties andtheir behavior under parameter variations are character-ized. An application to invariance entropy shows that theinformation needed to keep a system in a subset of the statespace is determined by the relatively invariant W -controlsets.
Ralph LettauUniversity of AugsburgResearch Unit Applied [email protected]
Fritz ColoniusUniversity of [email protected]
CP1
Nonlinear Unknown Input Observability: Analyti-cal Expression of the Observable Codistribution inthe Case of a Single Unknown Input
This paper investigates the unknown input observabilityfor nonlinear systems characterized by a single unknowninput and multiple known inputs. The goal is not to designnew observers but to provide a simple analytic conditionto check the observability of the state. In other words,the goal is to extend the observability rank condition tothe case of unknown input. As in the case of only knowninputs, the observable codistribution is obtained by recur-sively computing Lie derivatives along the vector fields thatcharacterize the dynamics. However, in correspondence ofthe unknown input, the corresponding vector field must berescaled. Additionally, the Lie derivatives must be alsocomputed along a new set of vector fields that are ob-tained by recursively performing suitable Lie bracketingof the vector fields that define the dynamics. The analyticapproach is illustrated by checking the weak local observ-ability of several nonlinear systems driven by known andunknown inputs.
Agostino [email protected]
CP2
Modelling and Stability for Interconnections of Hy-brid Systems
Robustness and stability theory of hybrid systems isstrongly developed recently, however interconnections ofsuch systems are poorly studied. The existing few resultshold under strong constraints on jump and flow sets ofsubsystems only. General type interconnections are notwell developed and raise many modelling and mathemati-cal problems. We will discuss these problems and possiblesolutions with emphasis on stability properties.
Petro Feketa, Sergey DashkovskiyUniversity of Applied Sciences Erfurt
[email protected], [email protected]
CP2
On Reduced Order Observer for Radiative Conduc-tive Heat Transfer Systems
This contribution deals with state observer design for aclass of non-linear coupled partial differential equationsthat describe radiative-conductive heat transfer systems in2D (two dimension). Observations are made though sen-sors placed at the upper boundary of the two dimensionaldomain. We explored the Galerkin method for a semi-discretization to obtain a large scale in finite dimensional.Thanks to the special structure of the obtained state sys-tem, we show through the Differential Mean Value Theo-rem that there always exists an observer gain matrix thatassures asymptotic convergence. Both full order and re-duced order state estimators are provided.
Mohamed GhattassiIECL-University of [email protected]
Mohamed Boutayeb, Jean Rodolphe RocheUniversity of [email protected], [email protected]
CP2
Instability Characterizations for Differential Inclu-sions
Instability of an equilibrium point has typically been de-fined as “not stable” rather than as a standalone property.This is, in part, due to the fact that several unstable be-haviors are possible. Furthermore, as the usual engineeringgoal is stability, all possible unstable behaviors are undesir-able. In this talk, we present some specific definitions forunstable equilibrium points for differential inclusions. Wealso present Lyapunov characterizations and discuss theirutility in a control design context.
Christopher M. KellettUniversity of [email protected]
CP2
Characterizations of Input-to-State Stability forInfinite-Dimensional Systems
This talk is devoted to Lyapunov characterizations ofthe input-to-state stability (ISS) property for infinite-dimensional control systems. We discuss Lyapunov charac-terizations of uniform asymptotic stability for systems withdisturbances and establish connections between the asymp-totic gain property, uniform global asymptotic stability ofundisturbed systems and ISS. Using the above criteria it ispossible to characterize input-to-state stability in terms ofISS Lyapunov functions.
Andrii Mironchenko, Fabian WirthUniversity of [email protected], fabian.wirth@uni-
CT15 Abstracts 53
passau.de
CP2
Eigenvectors of Nonlinear Maps on the Cone ofPositive Semidefinite Matrices and Application toStability Analysis
We show that the problem of synthesis of a common Lya-punov function for some classes of switched linear systemscan be approached by solving an eigenproblem involvinga nonlinear map on the cone of positive semidefinite ma-trices. This map involves the selection of a maximal lowerbound of a family of matrices in this cone. We present somevariants of the power algorithm, allowing one to solve thenonlinear eigenproblem in a scalable way.
Nikolas StottINRIA - CMAP, Ecole [email protected]
Xavier AllamigeonCMAP, Ecole [email protected]
Stephane GaubertINRIA-Saclay & CMAPEcole [email protected]
Eric Goubault, Sylvie PutotLIX, Ecole Polytechnique - [email protected], [email protected]
CP3
A New Inverse Optimal Control Method forDiscrete-Time Systems
This paper presents a new approach based on extendedkalman filter to construct a control lyapunov function. Thisfunction will be used in establishing the inverse optimalcontroller. The main aim of the inverse optimal controlmethod is to avoid the solution of HamiltonJacobiBellmanequation resulted from the traditional solution of nonlinearoptimal control problem. The relevance of the proposedscheme is illustrated through simulations. Results showthe effectiveness of the proposed method.
Moayed N. AlmobaiedIstanbul technical universityhttp://www.itu.edu.tr/en/[email protected]
Ibrahim Eksin, Mujde GuzelkayaIstanbul Technical UniversityControl and Automation [email protected], [email protected]
CP3
The Energy Czar’s Problem
Consider an island economy powered in part by renewableenergy, and in part by a single deposit of fossil fuel. Theislands energy czar, who wishes to make the best possibleuse of the endowment, faces an optimal control problem notunlike the one confronting the proprietor of an extractivefirm. The latter problem has an extensive history, whichwill be summarized. Existing results shed light on, but do
not completely solve, the energy czars problem.
James [email protected]
CP3
Trajectory Optimization and Performance-BasedVehicle Guidance in Spatiotemporally VaryingFields
We discuss planar trajectory optimization where the costfunctional is the integral along the trajectory of the inten-sity of a spatiotemporally-varying scalar field. We assumethat this spatial field is described by an advection-diffusionparabolic PDE or a Poisson-type elliptic PDE. Multiresolu-tion spatiotemporal discretization is employed for numer-ical trajectory optimization and for concurrent estimationof the field by a mobile sensor. Single- and twin-agent sce-narios will be considered.
Raghvendra V. CowlagiAssistant Professor, Worcester Polytechnic InstituteWorcester, MA, [email protected]
Michael A. DemetriouWorcester Polytechnic [email protected]
CP3
On the Optimal Control of the Rigid Body Pre-cise Movement: Is Energy Optimality the Same asTime Optimality?
For optimal control problems of rigid body precise move-ment minimal time optimality and minimal energy opti-mality are considered as competing approaches for trajec-tory planning. We investigate here theoretical and sim-ulation results showing that, with appropriate choice ofconstraints, these approaches are equivalent in the sensethat they produce the same trajectory. The optimal con-trol solver DIDO was used as a numerical tool.
Per-Olof GutmanFaculty of Civil and Environmental EngnTechnion-Israel Institute of [email protected]
Ilya IoslovichFaculty of Civil and Environmental EngineeringTechnion-Israel Institute of [email protected]
Shail MoshenbergFaculty of Civil and EnvironmentalEngineering, [email protected]
CP3
Optimal Control of Landfills
We tackle landfill optimization when the re-circulationleachate is the control. We propose a scheme to constructthe minimal time strategy by dividing the state space intothree subsets. On two of them the optimal control is con-stant until reaching target, while it can exhibit a singulararc on their complementary. The singular arc could have
54 CT15 Abstracts
a barrier, and we prove the existence of a switching curvethat passes through a point of prior saturation.
Alain [email protected]
Terence BayenUniversity Montpellier II, [email protected]
Matthieu SebbahUTFSM, Valparaiso, [email protected]
Andres Donoso-BravoCIRIC, Inria [email protected]
Alfredo TorricoCMM, Santiago, [email protected]
CP3
Minimal-Time Bioremediation of Water Resourceswith Two Patches
We study the bioremediation, in minimal time, of a waterresource using a single continuous bioreactor connected totwo pumps at different locations in the resource. This leadsto a minimal-time optimal control problem whose controlvariables are the inflow rates of both pumps, obtaining anon-convex problem. We solve the problem by applyingPontryagin’s principle to the associated generalized controlproblem and obtain explicit bounds on its value functionvia Hamilton-Jacobi-Bellman techniques.
Victor RiquelmeDIM, Universidad de Chile, Santiago, Chile,Universite Montpellier 2, Montpellier, [email protected]
Hector Ramırez C.DIM and CMM, Universidad de Chile,Santiago, [email protected]
Alain [email protected]
CP4
Stochastic Control Problem for Delayed SwitchingSystems with Restrictions
In this talk we consider optimal control problem forstochastic systems. Dynamic of the system is describedby the collection of stochastic differential equations withdelay. We have investigated the stochastic control systemwhich consist of several subsystems and a switching law in-dicating the active subsystem at each time instantly. Therestrictions is defined by the functional inclusions in theright ends of each time interval. Firstly, optimality condi-tion for control system without constraints is established.Then using Ekelands Variational Principle, the necessarycondition of optimality for restricted stochastic systems is
obtained .
Charkaz A. AghayevaInstitute of Cybernetics of ANAS, AzerbaijanAnadolu University, [email protected]
CP4
Geometric Methods for Optimal Sensor Design
Optimal estimation and control of linear systems are fun-damental to many areas of engineering and beyond. It iswell-known that the optimal estimator in the MSE sense isthe Kalman filter., the performance of which depends onthe observation matrix (C matrix) of the system. In thispresentation, we address the problem of finding the obser-vation matrix that yields the lowest estimation error. Thisproblem is non-convex, but we show almost global conver-gence to a global minimum in an appropriate regime.
Mohamed Ali BelabbasUniversity of [email protected]
CP4
On Discrete Time Optimal Portfolio for ContinuousTime Market Models
We present an algorithm of optimal multistock portfolioselection in the class of piecewise constant portfolios thatcan be restructured at a sequence of random times. Wesuggest to separate selection of an optimal redistributionof the risky stocks and the optimal distribution of fundsbetween risk free investment and the risky portfolio, Thisleads to a discrete time myopic optimal portfolio strategy.
Nikolai DokuchaevCurtin [email protected]
CP4
Stochastic Optimal Control with Delay in the Con-trol: Solution Through Partial Smoothing
Stochastic optimal control problems governed by delayequations with delay in the control are more difficult tostudy than the the ones when the delay appears only inthe state. The associated HJB equation does not satisfythe so-called “structure condition’ which means that “thenoise enter the system with the control’. The absence ofsuch condition, together with the lack of smoothing prop-erties which is a common feature of problems with delay,prevents the use of the known techniques to prove the exis-tence of regular solutions. In this paper we provide a resulton existence of regular solutions of such kind of HJB equa-tions and we use it to solve completely the correspondingcontrol problem finding optimal feedback controls. Themain tool used is a partial smoothing property that weprove for the transition semigroup associated to the un-controlled problem. Such results holds for a specific classof equations and data which arises naturally in many ap-plied problems.
Fausto GozziLuiss [email protected]
Federica MasieroUniversita di Milano Bicocca
CT15 Abstracts 55
CP4
Optimal Resource Extraction in Regime SwitchingLevy Markets
This paper studies the problem of optimally extractingnonrenewable natural resources in light of various financialand economical restrictions and constraints. Taking intoaccount the fact that the market values of the main naturalresources i.e. oil, natural gas, copper, gold, fluctuate ran-domly following global and seasonal macro-economic pa-rameters, these values are modeled using Markov switchingLevy processes. We formulate this problem as a finite-timehorizon combined optimal stopping and optimal controlproblem. We prove that the value function is the uniqueviscosity solution of the corresponding Hamilton-Jacobi-Bellman equations, and derive optimal extraction policies.Moreover, we prove the convergence of a finite differenceapproximation of the value function. Numerical examplesare presented to illustrate these results.
Moustapha PemyTowson UniversityDepartment of [email protected]
CP4
Stochastic Markov Decision Subject to Ambiguity
In this presentation we address optimality of stochasticcontrol strategies for infinite-horizon Markov decision prob-lems with discounted pay-off, when the controlled processconditional distribution belongs to a ball of radius R withrespect to total variation distance, centered at the nominalconditional distribution. The stochastic control problemis formulated using minimax theory and the following dy-namic programming equation is obtained
v(x) = infu∈U(x)
{f(x, u)+α
∫Xv(z)Qo(dz|x, u)+α
R
2
(supz∈X
v(z)− infz∈X
v(z))}
.
Here, v(x) is the value function, U(x) is the feasible con-trol set, f is the one stage cost, Qo(·|x, u) is the nominalcontrolled process conditional distribution and, α ∈ (0, 1)is the discounting factor.
Ioannis Tzortzis, Charalambos D. CharalambousDept of Electrical and Computer Engineering, Univ. [email protected], [email protected]
CP5
Computing the Hamiltonian Triangular Forms ofHamiltonian Pencils
This paper presents a new method for computing theHamiltonian triangular form of a Hamiltonian pencil λE−A with E,A ∈ R2n×2n without purely imaginary eigenval-ues. The algorithm is of computational complexity O(n3),and it is based on orthogonal-symplectic transformationsand thus preserves the Hamiltonian structure of the pencilλE−A. Problems in the existing benchmark collection forthe discrete-time algebraic Riccati equations are used toillustrate the performance of the proposed algorithm.
Delin ChuDepartment of Mathematics, National University ofSingapore
Block S17, 10 Lower Kent Ridge Road, Singapore [email protected]
CP5
Multigrid Preconditioning for Space-Time Dis-tributed Optimal Control Problems Constrainedby Parabolic Equations
We present some recent results regarding multigrid pre-conditioning of the linear systems arising in the solutionprocess of space-time distributed optimal control problemsconstrained by parabolic equations. While the constructionof the preconditioners is based on ideas extracted from op-timal control problems constrained by elliptic equations, inthe parabolic-constrained case the multigrid precondition-ers exhibit a suboptimal behavior, namely they approxi-mate the operators to be inverted by half an order lessthan optimal.
Andrei Draganescu, Mona HajghassemDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore [email protected], [email protected]
CP5
A Semi-Analytical Solution for the HelmholtzProblem in Three-Dimensional Case
This paper develops an analytical solution for sound, elec-tromagnetic or any other wave propagation described bythe Helmholtz equation. First, a theoretical investigationbased on Multipole Expansion method was established.Then, we evaluate numerically the theoretical solution ofscattering problem by an ideal rigid sphere. Finally, wemade a numerical study to present the variation of surfacepotential with respect to different physical parameters ofthe problem.
Layouni Amamou ManelRue Jomma Gharsallah, Touza 5023, [email protected]
CP5
Comparison between the MINC and MRMT Con-figurations: The n-dimensional Case
The models MINC (Multiple INteracting Continua) andMRMT (Multiple Rate Mass Transfer) are extensively usedin transport phenomena. We believe that these models arealso relevant to describe flows in soil or in porous media.In the same way, these models can be used to describe con-nections between bioreactors. The goal of this manuscriptis determine conditions for the input-output equivalence ofthese configurations for n compartments using some resultsof the linear system theory.
Alejandro Rojas-PalmaDepartamento de Ingeniera Matematica, Universidad [email protected]
Alain [email protected]
Jean-Raynald Dreuzy (de)Geosciences Rennes, UMR CNRS 6118, Rennes, FranceIDAEA-CSIC, Barcelona, Spain.
56 CT15 Abstracts
Hector RamırezCentro de Modelamiento, Matematico-Universidad [email protected]
CP5
Extracting Motion Primitives Toward PlanningHuman-Like Motions
The motions of entities can be thought of as either short-or long-term motion primitives: fragments of movementsthat embody one or more significant actions. We present ameans of quickly and automatically extracting these promi-nent actions from long sequences of human movement andpose data. We show that dynamical-systems-based char-acterizations of these primitives can be used to efficientlyplan paths for a highly articulated humanoid platform.
Isaac J. SledgeDepartment of Electrical and Computer EngineeringUniversity of [email protected]
Kamran MohseniUniversity of Florida, Gainesville, [email protected]
CP5
Regulation Pitch Angle of Wind Turbine UsingReference Model Adaptive Controller
The conversion of wind energy to electrical energy withwind turbine is one of the best ways for reduction of harm-ful effects of fossil fuels. The renewable energy is growingrapidly in all over the world. Controlling blade pitch angleis a suitable way to achieve desired power of the turbine atlow speed winds and in order to prevent damages in strongwind conditions. In this paper, pitch angle control in dif-ferent wind conditions by using Reference Model Adaptive(RMA) Controller is proposed. Simulations and numericalresults show that the output power control and pitch anglebased on RMAC has faster nominal value with less error.
Alireza YazdizadeShahid Beheshti UniversityA [email protected]
CP6
Frequency Identification of Wiener-HammersteinSystems.
The problem of identifying Wiener-Hammerstein systemsis addressed in the presence of two linear subsystems ofstructure totally unknown. Presently, the nonlinear ele-ment is allowed to be noninvertible. The system identifica-tion problem is dealt by developing a two-stage frequencyidentification method such a set of points of the nonlin-earity are estimated first. Then, the frequency gains ofthe two linear subsystems are determined at a number offrequencies. The method involves Fourier series decom-position and only requires periodic excitation signals. Allinvolved estimators are shown to be consistent.
Adil BrouriENSAM, AEEE departm, L2MC, Moulay IsmailUniversity, Meknes
Moroccobrouri [email protected]
CP6
Frequency-Domain Performance Analysis ofDistributed-Parameter Systems under PeriodicSampled-Data Feedback Control
The stability and performance of distributed-parametersystems operating under periodic sampled-data feedbackcontrol is studied via integral-quadratic constraint (IQC)based analysis. Sufficient frequency-domain conditionsare derived for verifying a specified bound on the L2-gain of the feedback interconnection of a plant with (ir-rational) Callier-Desoer class transfer function and a feed-back controller obtained via the periodic sample-and-holddiscretization of a finite-dimensional LTI controller. Theanalysis is underpinned by a time-varying delay model ofthe sample-and-hold operation and IQC characterizationsof a related system. An illustrative numerical example in-volving the control of a linear system of hyperbolic conser-vation laws is presented.
Chung-Yao KaoNational Sun Yat-Sen University, [email protected]
Michael CantoniUniversity of [email protected]
CP6
Optimization of Synchronization Gains in Net-worked Distributed Parameter Systems
We consider networked distributed parameter systems thatare tasked with synchronization. Synchronization con-trollers based on static output feedback are used to ensuresynchronization. Using both tracking and synchronizationmetrics, the gain optimization problem is formulated as aminimization of a quadratic performance index. The op-timal gains are then found as the ones that minimize thetrace to the solution of a parameter-dependent operatorLyapunov equation for the aggregate system.
Michael A. DemetriouWorcester Polytechnic [email protected]
CP6
Right Coprime Factorizations for Fractional Sys-tems with Input Delays
The design of robust control laws lies in the computationof left and right coprime factorizations over the ring ofcomplex functions that are analytic in the right complexplane. In her recent thesis, the third author (by alpha-betic order) described a method to compute left coprimefactorizations for a class of fractional systems with inputdelays. Here is proposed a method to compute right co-prime factorizations. The method is based on the conceptof column-reduced matrix, that already proved to be use-ful to solve this problem in the case of finite dimensionalsystems.
Jean Jacques LoiseauIRCCyN Nantes, [email protected]
CT15 Abstracts 57
Catherine BonnetTeam DISCO, INRIA Saclay, [email protected]
Le Ha Vy NguyenTeam DISCO, INRIA Saclayand Math. Dept., Univ. [email protected]
CP6
Flow Sensing and Control for Aerospace Vehicles
Aerospace vehicles move in a fluid such as water or air,which can be moving relative to an inertial frame. Themovement of fluid over the vehicle impacts the dynamicsand control of translational and rotational motion. To im-prove control performance, the flow can be characterizedin real time by assimilating spatially distributed measure-ments of pressure and/or velocity. The design and use offlow sensing arrays for underwater and aerial vehicles willbe described.
Derek A. PaleyUniversity of MarylandDept. Aerospace Engineering and Inst. for [email protected]
CP6
On Robust Output Regulation for Continuous-Time Periodic Systems
We construct a controller to solve robust output trackingproblem for a stable linear continuous-time periodic systemon a finite-dimensional space. We begin by transformingthe time-dependent plant to a time-invariant discrete-timesystem using the “lifting technique’. The controller is thendesigned to achieve robust output tracking for the liftedsystem. We show that the solution of the control problemfor a continuous-time periodic system necessarily requiresan error feedback controller with an infinite-dimensionalinternal model. The results are illustrated with an exam-ple where robust output tracking is considered for a stableperiodic scalar system.
Lassi PaunonenDepartment of MathematicsTampere University of [email protected]
CP7
Parameter Estimation for Nonlinear Immune Re-sponse Model Using Em
The problem of parameter estimation of reduced mathe-matical model of the acute inflammatory response is con-sidered for the discrete case in the presence of disturbancesand measurement noise. A method combining expectationmaximization and particle filter is introduced. the param-eters that characterize each virtual patient are of interest.We begin with a study of nonlinear observability of thesystem to justify the use of state estimation and finally wepresent some simulation and discuss the obtained results.
Ouassim BaraUniversity of Tennessee at [email protected]
Judy DayUniversity of [email protected]
Seddik DjouadiUniversity of Tennessee at knoxvilleDepartment of Electrical engineering and [email protected]
CP7
Characterization of the Hemodynamic Response inthe Brain using Observer
Cerebral blood flow (CBF) is a key physiological variablein understanding the hemodynamic response in the brainwhich gives a deep insight into the underlying dynamicsof brain activation. We propose an observer-based ap-proach to estimate CBF from blood oxygen level dependent(BOLD) signal measured using functional magnetic reso-nance imaging. The model describing the pathway fromCBF to BOLD is a coupled system of partial and ordi-nary differential equations (PDE/ODE). Numerical resultswill be presented to show the accuracy of the estimationmethod.
Zehor BelkhatirComputer, Electrical and Mathematical Sciences andEngineering, [email protected]
CP7
Optimal Dosing Strategies Against Susceptible andResistant Bacteria
Antibiotic modelling is concerned with the problem of find-ing efficient and successful dosing techniques against bac-terial infections. In this study, we model the problem oftreating a bacterial infection where the bacteria is dividedinto two sub-populations: susceptible and resistant. Thesusceptible type may acquire the resistance gene via theprocess of conjugation with a resistant bacterium cell. Ef-ficient treatment strategies are devised that ensure bac-teria elimination while minimizing the quantity of antibi-otic used. Such treatments are necessary to decrease thechances of further development of resistance in bacteriaand to minimize the overall treatment cost. We considerthe cases of varying antibiotic costs, different initial bac-terial densities and bacterial attachment to solid surfaces,and obtain the optimal strategies for all the cases. The re-sults show that the optimal treatments ensure disinfectionfor a wide range of scenarios.
Mudassar ImranArizona State [email protected]
CP7
A Mathematical Analog of Muscular Hydrostatsand Similar Tissues
Muscular hydrostats (tongues, trunks, and tentacles) arecomposed almost of muscles which can shorten themselvesbut require a force external to the muscle to lengthen.This external force is supplied by the internal pressurethat maintains the constant volume of the structure. Avery simplified mathematical description of such a systemis proposed and its response to various controls is computed
58 CT15 Abstracts
and displayed. Curling a tentacle, a trunk, or a tongue isdemonstrated.
William S. LevineUniversity of Maryland, College [email protected]
CP7
A Variable Reference Trajectory for Model-FreeGlycemia Regulation
The control design of an artificial pancreas, which is a hotresearch topic for diabetes studies, is tackled via the newlyintroduced model-free control and its corresponding intelli-gent proportional controller, which were already quite suc-cessful in many concrete and diverse situations. It resultsin an insulin injection for type 1 diabetes which displaysvia constant references a good nocturnal/fasting response,but unfortunately poor postprandial behavior due to longhyperglycemia. When a variable reference is introduced,that switches between a constant one, when glycemia ismore or less normal or moderate, and an exponential decayreference path, when a high glycemia rate indicates a mealintake, the results in silico, which employ real clinical data,become excellent. We obtain a bolus-shaped insulin injec-tion rate during postprandial phases. The hyperglycemicpeaks are therefore lowered a lot.
Taghreed MohammadridhaPhD student at IRCCyN-Ecole Centrale de [email protected]
Claude MoogLUNAM, IRCCyN (CNRS, UMR 6597)[email protected]
Emmaneul DelaleauInstitut Superieur de lElectronique et du Numerique(ISEN)[email protected]
Michel FliessLIX (CNRS, UMR 7161) Ecole polytechnique-ParisALIEN(Algebre pour Identification & EstimationNumeriques)[email protected]
Cedric JoinCRAN (CNRS, UMR 7039), Universite deLorraine-NancyALIEN(Algebre pour Identification & EstimationNumeriques)[email protected]
CP8
Diffusive Realization of a Lyapunov Equation So-lution, and Parallel Algorithms Implementation
In a previous work, a theoretical framework of diffusiverealization for state-realizations of some linear operatorshave been developed. Those are solutions to certain linearoperator differential equations posed in one-dimensionalbounded domains. They illustrate the theory on a Lya-punov equation arising from optimal control theory of theheat equation. In principle their method might be veryefficient for real-time computation, however it is suffering
from strong limitations. Here, we present significant im-provements and report numerical results. A method ofcontour optimization is provided. It is based on a theo-retical error estimate of the solution. Finally, we discussexpected gains if the method is implemented on differentparallel computer topologies. The envisioned applicationsare for real-time distributed control on distributed com-puting architectures.
Raphael CouturierIUT [email protected]
CP8
On Controllability of a Two-Dimensional Networkof Ferromagnetic Ellipsoidal Samples
In this article, we address the problem of stability andcontrollability of two-dimensional network of ferromagneticparticles of ellipsoidal shapes. The control is the magneticfield generated by a dipole whose position and amplitudecan be selected. In the absence of control, first we prove theexponential stability of the relevant configurations of thenetwork. Then, we investigate the controllability by themeans of external magnetic field induced by the magneticdipole.
Sharad Dwivedi, Shruti DubeyIndian Institute of Technology [email protected], [email protected]
CP8
Analysis of the Push-Sum Algorithm for UnreliableNetworks
In multi-agent systems, the push-sum algorithm allowscomputing the average of values held by the agents in a de-centralized way. Unlike classical methods, push-sum alsoworks when communications are directed or asynchronous.When the network is unreliable, the computed value willdeviate from the true average. We analyze the error ofthe final common value obtained, both theoretically andnumerically, and compare it with the standard consensusalgorithm.
Balazs Gerencser, Julien HendrickxUniversite catholique de [email protected],[email protected]
CP8
Minimal Data Rates and Entropy in Digitally Net-worked Systems
In digitally networked control systems the assumption ofclassical control theory that information can be transmit-ted instantaneously, lossless and with arbitrary precision isviolated. This raises the question about the smallest datarate above which a given control task can be solved. For theproblem to render a subset Q of the state space invariant,the minimal data rate can be described by an entropy-likequantity, the so-called invariance entropy. If one consid-ers a single feedback loop and assumes that the system iscompletely controllable and uniformly hyperbolic on Q, theinvariance entropy can be expressed in terms of Lyapunovexponents. For networks with several subsystems there aredifferent possibilities to formulate the question about thesmallest data rate for the invariance problem, but also in
CT15 Abstracts 59
this setting entropy-like quantities can be introduced tosolve the problem.
Christoph KawanInstitute of MathematicsUniversity of [email protected]
Jean-Charles DelvenneUniversite Catholique de LouvainApplied Mathematics [email protected]
CP8
Real-Time Decentralized and Robust Voltage Con-trol in Distribution Networks
Voltage control plays an important role in the operationof electricity distribution networks, especially when thereis a large penetration of renewable energy resources. Inthis paper, we focus on voltage control through reactivepower compensation and study how different informationstructures affect the control performance. In particular, wefirst show that using only voltage measurements to deter-mine reactive power compensation is insufficient to main-tain voltage in the acceptable range. Then we propose twofully decentralized and robust algorithms by adding addi-tional information, which can stabilize the voltage in theacceptable range. The one with higher complexity can fur-ther minimize a cost of reactive power compensation in aparticular form. Both of the two algorithms use only localmeasurements and local variables and require no communi-cation. In addition, the two algorithms are robust againstheterogeneous update rates and delays.
Guannan Qu, Na LiHarvard [email protected], [email protected]
Munther [email protected]
CP8
Topological Obstructions to Distributed FeedbackStabilization to a Submanifold
We consider the problem of local asymptotic feedback sta-bilization – via a C1 feedback law – of a control systemx = f(x,u) defined in Euclidean space Rn (with f ∈ C1)to a compact, connected, oriented p−dimensional subman-ifold P of Rn, subject to the constraint that the scalarentries of the system function f and of the feedback law udepend only on selected subsets of the state variables. Suchconstraints arise naturally in the context of distributed con-trol systems, typically consisting of multiple agents withonly local communication between the various agents. Weobtain topological necessary conditions for the existenceof such a stabilizing feedback control law; these topologi-cal conditions are expressed in terms of the generators ofthe homology groups of certain topological spaces natu-rally associated with the control problem, as well as thetopology of the submanifold to which stabilization is to beperformed.
Abdol-Reza MansouriDepartment of Mathematics and StatisticsQueen’s University
CP9
Sampling Intervals Enlargement for a Class ofParabolic Sampled-Data Observers
Enlarging the sampling intervals in the networked control-estimation is a hot topic. Presently, we seek sampling in-terval enlargement for sampled-data observers designed fora class of parabolic systems. This purpose is shown to beachievable by using inter-sample output predictor basedobservers. Sufficient conditions for global exponential con-vergence are derived in terms of LMIs via Lyapunov-Krasvoskii functionals. It is checked through simple ex-amples that the proposed observers considerably enlargethe sampling interval. The results are illustrated by someexamples from the literature.
Tarek Ahmed-AliGREYC LabENSICAENahmed [email protected]
Emilia FridmanTel Aviv University, [email protected]
Fouad GiriGREYC LabUniversite de Caen [email protected]
Francoise Lamnabhi-LagarrigueLSS [email protected]
CP9
Reduced Order Modelling for Optimal CancerTreatment
We study reduced order modelling for optimal treatmentplanning. Boltzmann transport equation is used to modelthe interaction between radiative particles with tissue. Atfirst, we solve optimization problems: minimizing the de-viation from desired dose distribution. Then we consider aparameterized geometry. In offline stage we solve a prob-lem for sampled parameter values. The online phase thenconsists of solving the reduced problem for the actual setof parameters. Theoretical and numerical results are pre-sented.
Bahodir AhmedovAachen Institute for Advanced Study inComputational Engineering Science (AICES)[email protected]
Michael Herty, Martin GreplRWTH Aachen [email protected], [email protected]
CP9
Some Numerical Extension for the LOI/BOI Ap-proach for the Control of de Saint-Venant Equa-tions in Infinite Dimension
This paper considers the control design of a nonlinear dis-tributed parameter system in infinite dimension, described
60 CT15 Abstracts
by PDEs of de Saint-Venant. The nonlinear system dy-namic is formulated by a Multi-Models approach over awide operating range, where each local model is definedaround a set of operating regimes. A PI feedback was de-signed and performed through Bilinear Operator Inequalityand Linear Operator Inequality techniques for infinite di-mensional systems. The authors propose in this paper toimprove the numerical part by introducing weight μi notonly equal to {0,1}, but μi ∈ [0, 1].
Valerie Dos Santos MartinsUniversity Claude Bernand of Lyon [email protected]
Mickael RodriguesUniversite Claude Bernard Lyon [email protected]
CP9
Optimal Damping Coefficient of a Slowly RotatingTimoshenko Beam
This paper continues the authors previous investigationsof stability of the slowly rotating Timoshenko beam whosemovement is controlled by the angular acceleration of thedisk of the driving motor into which the beam is rigidlyclamped. We consider the problem of optimal value ofdamping coefficient of a particular type of viscoelasticdamping operator. To determine location of spectrum ofan appropriate operator we use a transfer function method.
Mateusz FirkowskiUniversity of [email protected]
Jaroslaw WozniakUniversity of SzczecinDep. Mathematics and [email protected]
CP9
Asymptotic Behavior for Coupled Abstract Evolu-tion Equations with One In?nite Memory
In this work, we consider two coupled abstract linear evo-lution equations with one in?nite memory acting on the?rst equation. Under a boundeness condition on the pasthistory data, we prove that the stability of our abstractsystem holds for convolution kernels having much weakdecays than the exponential one considered in the liter-ature. The general and precise decay estimate of solutionwe obtain depends on the growth of the convolution kernelat in?nity and the regularity of the initial data. We alsopresent various applications to some hyperbolic distributedcoupled systems such as wave-wave, Petrovsky-Petrovsky,wave-Petrovsky and elasticity-elasticity. These results havebeen published in Applicable Analysis, 2014.
Aissa GuesmiaInstitut Elie Cartan de Lorraine, Universite de LorraineBat. A, Ile du Saulcy, 57045 Metz cedex 01, [email protected]
CP9
Observer-based Bilinear Control of First-order Hy-
perbolic PDEs
We investigate the problem of bilinear control of a solarcollector plant using available boundary and solar irradi-ance measurements. The solar collector is described by afirst-order 1D hyperbolic partial differential equation wherethe pump volumetric flow rate acts as the control input.By combining a boundary state observer and an internalenergy-based control law, a nonlinear observer based feed-back controller is proposed. The effect of solar radiation iscancelled using a feed-forward control term.
Sarah Mechhoud, Shahrazed Elmetennani, Meriem [email protected],[email protected], [email protected]
CP10
Rigorous Numerical Method for Irrigation CanalSystem Dynamics and Control
Water canals for water delivery or irrigation provide achallenging system dynamics and control problem for dis-tributed parameter plants. Water pool dynamics are de-rived from the shallow water equations (also called Saint-Venant equations in its one-dimensional form) that are aset of hyperbolic partial differential nonlinear equations.Rigorous numerical methods that are able to capture wa-ter wave dynamics in canals are difficult to achieve. In thiscase a numerical routine was designed from a finite vol-ume method for hyperbolic systems of conservation lawswith source terms using a semi-discrete MUSCL flux re-construction linear well-balanced scheme. Time integra-tion was done with a Runge-Kutta method. The numericalmethod was used to simulate water dynamics in the firsttwo pools with withdraws of an existing irrigation canal inVila Nova de Mil-Fontes, Portugal, including PI controlledgates movement to compensate for wave disturbances.
Jose [email protected]
CP10
Preconditioned Continuation Model PredictiveControl
Model predictive control (MPC) anticipates future eventsto take appropriate control actions. Nonlinear MPC(NMPC) describes systems with nonlinear models and/orconstraints. A Continuation/GMRES Method for NMPC,suggested by T. Ohtsuka in 2004, uses GMRES iterative al-gorithm to solve a forward difference approximationAx = bof the Continuation NMPC (CNMPC) equations on everytime step. The coefficient matrix A of the linear systemis often ill-conditioned, resulting in poor GMRES conver-gence, slowing down the on-line computation of the con-trol by CNMPC, and reducing control quality. We adoptCNMPC for challenging minimum-time problems, and im-prove performance by introducing efficient preconditioning,utilizing parallel computing, and substituting MINRES forGMRES.
Andrew Knyazev
Mitsubishi Electric Research Labs (MERL)[email protected]
CT15 Abstracts 61
Yuta FujiiAdvanced Technology R&D Center, Mitsubishi [email protected]
Alexander MalyshevMitsubishi Electric Research Labs (MERL)[email protected]
CP10
Anfis Based Software Development for Nonlinearwith Time Delay Dynamic Systems Identification
This article aims to show a software that was developed toidentify nonlinear dynamical systems with time delay us-ing the ANFIS. Therefore, we conducted two tests in thesoftware, a simulated test uses a benchmark function, theMackey-Glass, for making the prediction of future valuesof time series. The second test was performed using a realsystem coupled tanks with a smooth nonlinearity and timedelay for the purpose to identify the dynamics of the sys-tem. The results shown in this paper confirm the capabilityof the developed software to identify nonlinear, with timedelay, dynamic systems on a simple and intuitive way, asit was proposed.
Jose K. Martins, Fabio Souza, Fabio ArajoUniversidade Federal do Rio Grande do NorteDepartamento de Engenharia da Computacao eAutomacaojk [email protected], [email protected],[email protected]
CP10
New Approach to Implicit Systems and Applica-tions in Control Methods for Optimal Design Prob-lems
Implicit representations of domains are at the core of fixeddomain methods in shape optimization, like control meth-ods or the fictitious domain approach. When the govern-ing equation has Dirichlet boundary conditions, there arealready known results in this respect. In the case of Neu-mann boundary conditions or of boundary observation, amore detailed knowledge of the properties of the unknown(implicitly defined) boundaries is necessary. We shallpresent a new approach based on implicit parametrizationsof the boundaries. It also allows the handling of the criticalcase via the generalized solutions. We consider a class ofvariations of the unknown shapes, called functional varia-tions, similar to the Dirichlet case and show how to com-pute directional derivatives of the unknown geometry.
Dan I. TibaInstitute of Mathematics, Romanian AcademyBucharest, [email protected]
CP10
Accelerated Gradient Methods for Elliptic OptimalControl Problems with Tv-Regularised Cost
Over the past years, first order gradient methods have re-gained significant attention. Algorithms like FISTA areapplicable to a broad range of scenarios, converge quicklyand are ideally suited for large-scale problems. In this talk,we consider optimal control problems governed by ellip-tic equations, with a focus on non-smooth cost function-
als. We will demonstrate how fast or accelerated gradientmethods can be advantageously employed to solve theseproblems very efficiently.
Timm Treskatis, Miguel Moyers-Gonzalez, Chris PriceSchool of Mathematics and StatisticsUniversity of [email protected],[email protected],[email protected]
CP10
A Kind of Formula For Computing the MatrixFunction
In this paper we employ the symbolic computation to de-rive a kind of formula for computing the matrix functionf(A).
Zhinan ZhangCollege of Mathematics and System ScienceXinjiang University, Xinjiang, [email protected]
CP11
New Results on Stochastic Consensus Networks
We revisit the genera linear time varying consensus prob-lem and provide new conditions for asymptotic agreementon the agents’ states on two distinct types of stochasticversions of the distributed algorithm. The first type is alinear discrete time dynamic evolution with connectivitysignals driven by a measure preserving dynamical system.Our result highlights the fact that the probabilistic na-ture of the connections among agents that imposes almostsure convergence to consensus actually reproduces the de-terministic recurrent connectivity condition known in theliterature. The second type, is a linear continuous timeflocking model with multiple time-varying diffusion coeffi-cients. Via a stability in variation argument we establishsufficient conditions for asymptotic flocking with coordi-nation around around a random-variable. Our analysis isbased on rate at which the diffusion compartment vanishes.We argue, by example, that our results treat a number ofrelated models proposed in the literature, as special cases.
Christoforos SomarakisThe Institute For Systems ResearchUniversity of Maryland, College [email protected]
John BarasUniv. MarylandCollege [email protected]
CP11
A Projection-Based Dual Algorithm for Fast Com-putation of Control in Microgrids
We present a novel algorithm for the distributed computa-tion of optimal predictive storage and reactive power con-trol in microgrids. This algorithm uses a dual decomposi-tion approach to deal with coupling constraints, and a pri-mal projection procedure to handle local constraints. Thissignificantly decreases the amount of iterations needed forpractical convergence, as compared to the dual decomposi-
62 CT15 Abstracts
tion algorithm involving all constraints. Simulations com-pare the algorithm with the dual decomposition approachin four different testbeds, to show how the speed of con-vergence is improved.
Andres CortesUniversity of California, San [email protected]
Sonia MartinezUniversity of California, San DiegoDepartment of Mechanical and Aerospace [email protected]
CP11
Nullspace Design of Configuration Matrices forLyapunov-Based, Multi-Vehicle Control
Lyapunov potential functions are common in multi-vehiclecontrol algorithms because they ensure vehicle coordi-nation while incorporating inter-vehicle communicationtopologies. However, this control approach often requiresall vehicles to converge to a desired phase or shape variable.This talk will present recent results toward the design ofnovel quadratic functions for prescribed coordination. Bydesigning quadratic terms based on matrices with a de-sired nullspace, we derive multi-vehicle control algorithmssteering vehicles to any relative configuration.
Levi DeVriesUnited States Naval AcademyDepartment of Weapons and Systems [email protected]
CP11
Convergence of Iterative Co-Learning Control
This talk discusses iterative co-learning where multiple lin-ear subsystems update their input simultaneously based onthe error in a common desired output. A challenge is thatconvergence of iterative learning for each individual sub-system (when the other subsystems are not learning) maynot guarantee convergence under co-learning. Co learn-ing with an update-partitioning approach will be presentedthat guarantees convergence whenever the individual, iter-ative learning for each subsystem is convergent.
Santosh DevasiaUniversity of [email protected]
CP11
Role of Structured Noise in Emergence of Funda-mental Tradeoffs in Linear Dynamical Networks
We deal with a network of multiple agents with dynam-ics described by a continuous time linear consensus algo-rithm. The performance of the network in presence of var-ious types of noise inputs is investigated. We adopt the ex-pected steady-state dispersion of the states of the networkas a performance measure. The relationship between thisperformance measure and characteristics of the underlyinggraph of the network is explored. Specifically, we quantifyhow the asymptotic behavior of a linear consensus networkis influenced by the existence of structured noises in dif-ferent elements of the network, such as noise in sensors,emitters, channels, receivers, and the computational unit.In the next step, a class of centrality measures is introduced
in order to assess the role of each agent and channel withina network. Finally, we discuss the emergence of fundamen-tal tradeoffs on the performance measure with respect tothe effects of structured noises in different elements of thenetwork.
Milad Siami, Sadegh Bolouki, Nader MoteeLehigh [email protected], [email protected], [email protected]
CP11
Robust Dynamic Tolls for Self-Interested TrafficRouting
We consider the problem of designing robust taxation-mechanisms for influencing self-interested behavior inrouting-problems where users have unknown sensitivitiesto taxes. Classical results are not sufficient for addressingthis question due to unrealistic assumptions on either thesystem condition (i.e., homogeneous known sensitivities)or available information (i.e., network demands and userssensitivities). Accordingly, we present a dynamic tollingmechanism that, using local feedback, provably guaranteessystem-wide optimal behavior for a well-studied class ofrouting-problems.
Andreas WachterUniversity of StuttgartUniversity of Colorado at [email protected]
Jason MardenUniversity of Colorado, [email protected]
CP12
Optimal Inventory in Failure-Prone ManufacturingSystems with Monomial Holding Costs
The optimal policy for the production plan for a singlecommodity in a failure-prone parallel machine system isdetermined by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The system is assumed to possesstwo levels of operation capacity and the surplus holdingcost is a monomial function. In this paper the analyticalmethod based on Akella and Kumar (1986) is developed tosolve the HJB equation using the derived boundary condi-tions of the value function. The effect of different operatingparameters, such as failure rate, repair rate, maximal ca-pacity level, et. al., on the optimal inventory level andthe value function are numerically computed by using ouranalytical formula. For an arbitrary hold cost with the an-alytical or empirical formula which can be approximated bythe sum of monomial functions, thus this paper providesa way to construct the corresponding optimal productionplan.
Huang-Nan HuangDepartment of MathematicsTunghai [email protected]
Shu-Yi TuMathematics Department, University of [email protected]
CP12
Performance Bound for Approximate Dynamic
CT15 Abstracts 63
Programming in Borel Spaces
We consider discrete-time constrained Markov control pro-cesses (MCPs) for Borel state and action spaces. Wepresent a two-stage method to approximate the optimalvalue of the constrained MCPs via finite-dimensional con-vex optimization programs. The main contribution of thisstudy is to provide explicit error bounds for the proposedsolution under mild assumptions which are investigated forthe long-run discounted as well as average cost. Finally, wealso discuss the performance of the approximated controlpolicy.
Peyman Mohajerin Esfahani
Swiss Federal Institute of Technology (ETH) in [email protected]
Tobias SutterETH [email protected]
Daniel KuhnEcole Polytechnique Federale de [email protected]
John LygerosETH [email protected]
CP12
Improvements to Optimal Control Problem Solverson the Example of a Reachable Set Algorithm
The reachable set at a given time T of a nonlinear controlsystem is the union of endpoints of all feasible solutions.The talk illustrates how an OCP-solver can be applied tocalculate discrete reachable sets and shows some strategiesto increase the stability of the OCP-solver for this class ofproblems. Furthermore a subdivision approach to improvethe performance of the algorithm will be introduced.
Wolfgang RiedlDepartment of MathematicsUniversity of [email protected]
CP12
Convex Methods for Rank-Constrained Optimiza-tion Problems
Consider a rank-constrained optimization problem, whichis otherwise convex. Penalizing the nuclear norm of thematrix minimizes its rank. We introduce a convex con-straint, which, when used in conjunction with the abovepenalty, results in a convex problem that usually yields so-lutions of exactly desired rank. A modified dual programfinds the ”best” value of the parameter used with the nu-clear norm. It is shown that allowing negative valued pa-rameters (rewarding the nuclear norm) can result in betterperformance. The methods are demonstrated on SDPs.
Michael Rotkowitz, Van Sy Mai, Dipankar Maity,Bhaskar RamasubramanianElectrical and Computer EngineeringUniversity of Maryland, College [email protected], [email protected], [email protected], rb-
CP12
Distributed Optimization Based on Multi-AgentSystems
First, a continuous-time multi-agent system with nonlin-ear coupling is proposed to solve distributed optimizationproblems. Sufficient conditions are derived to ascertainthe convergence to optimal solutions. The nonlinear cou-pling can deal with bounded inputs for agents and lim-ited bandwidth for communication among agents. Fur-thermore, the nonlinear coupling has a superior propertyof robustness against additive noise than the linear case.Next, communication delays are considered on multi-agentsystems for distributed optimization. Based on optimalityconditions, it is revealed that optimal solutions are corre-sponding to the equilibrium points in a positive invariantset of the time-delay system. Both delay-dependent anddelay-independent sufficient conditions are derived for as-certaining convergence to optimal solutions in the case ofslow-varying delay. Delay-dependent conditions are alsopresented for the case of fast-varying delays.
Jun Wang, Shaofu YangThe Chinese University of Hong [email protected], [email protected]
Qingshan LiuHuazhong University of Science & [email protected]
CP13
Output Feedback H-infinity Control for Discrete-Time Singular Systems: A Strict LMI Approach
This paper deals with the problem of the output feedbackH∞ control for discrete-time singular systems. Our goal isto develop a numerically tractable controller design methodfor output feedback H∞ control of discrete-time singularsystems. First, a new sufficient condition for H∞ per-formance is derived. Then, a sufficient condition for theexistence of the desired output feedback H∞ controller isestablished. The proposed controller design method is for-mulated under the strict LMI framework. Finally, a nu-merical example is used to demonstrate the effectiveness ofpresented method.
Shyh-Feng ChenChina University of Science and [email protected]
CP13
Parameterization of Positively Stabilizing Feed-backs for Single-Input Positive Systems
For unstable positive finite-difference systems approximat-ing a diffusion PDE system with Neumann boundary con-ditions and scalar boundary input, parameterizations of allpositively stabilizing state feedbacks are derived.They arebased on characterizations of stable Metzler matrices byLMIs and of polyhedral sets as finitely generated cones, re-spectively.With well-chosen parameter values, this processgenerates a Dirac sequence of feedback functionals yieldinga limit feedback such that the resulting closed-loop PDEsystem is positive and stable.
Jonathan N. Dehaye, Joseph J. Winkin
64 CT15 Abstracts
University of Namur, Department of MathematicsNamur Center for Complex Systems (naXys)[email protected], [email protected]
CP13
On the Construction of Continuous SuboptimalFeedback Laws
It is well known that optimal feedback laws are usually dis-continuous functions on the state, which yields to ill-posedclosed loop systems and robustness issues. In this talk weshow a procedure for the construction of a continuous sub-optimal feedback law that allows overcoming the aforesaidproblems. The construction we exhibit depends exclusivelyon the initial data that could be obtained from the optimalfeedback.
Cristopher HermosillaENSTA [email protected]
Fabio AnconaUniversita degli Studi di [email protected]
CP13
A Topological Method for Finding Positive Invari-ant Sets
A usual way to find invariant sets of a differential systemis to impose that the flow goes inward on the border ofthe set. Using a topological approach (and in particularWazewskis property) we present an algorithm that is basedon a sufficient and weaker combinatorial condition of theflow on the border. We start from a template polyhedronand prove the positive invariance of a subset in the interiorof this template.
Sameh MohamedLSV (ENS Cachan) and LIX (Ecole Polytechnique)[email protected]
Laurent FribourgLSV (E.N.S Cachan)[email protected]
Sylvie Putot, Eric GoubaultLIX, Ecole Polytechnique - [email protected], [email protected]
CP13
A Graph-Related Sufficient Condition for the Ex-act Computation of the Joint Spectral Radius
Our talk relates to the stability analysis of discrete-timeswitching systems, with and without logical switching con-traints. We present an efficiently checkable sufficient con-dition under which a quadratic multiple Lyapunov functionhas a contractivity factor equal to the joint spectral radiusof a system. This allows us to exactly compute its jointspectral radius in finite time. We put our work in rela-tion with the previously introduced finite-time algorithmof Guglielmi and Protasov.
Matthew PhilippeUniversite Catholique de Louvain,ICTEAM/ [email protected]
Raphael JungersUniversite Catholique de Louvain,ICTEAM/[email protected]
CP13
Convexity + Curvature: Tools for the Global Stabi-lization of Nonlinear Systems with Control InputsSubject to Magnitude and Rate Bounds
The aim of this paper is to address the global asymptoticstabilization (GAS) of affine systems with control inputssubject to magnitude and rate bounds, in the frameworkof Artstein-Sontag’s control Lyapunov function (CLF) ap-proach. These bounds are defined by compact (convex)control value sets (CVS) U with 0 ∈ intU . Convex Analy-sis together with Differential Geometry allow us to revealthe intrinsic geometry involved in the CLF stabilizationproblem, and to solve it, if an optimal control ω(x) exists.The existence and uniqueness of ω(x) depends on convexityproperties of CVS U ; whereas its regularity and bounded-ness of its differential is achieved in terms of the curvatureof U . However, in view that control ω(x) is singular, weredesign it to derive an explicit formula for regular damp-ing feedback controls fulfilling magnitude and rate boundsthat render GAS a class of affine systems.
Julio Solis-DaunUniversidad Autonoma Metropolitana - [email protected]
CP14
Thermostatic Approximation of Optimal ControlProblems on Multi-Domains
We study an optimal control problem with two controlleddifferent dynamics in two half-spaces, in the framework ofHJB equations. We introduce an approximation by the useof switching rules of the delayed-relay type, and study thepassage to the limit when the parameter of the approxima-tion (i.e. the thresholds distance) goes to zero. We thencompare our result with other ones from the recent litera-ture. Finally, we briefly sketch a one-dimensional threefoldjunction problem.
Fabio Bagagiolo, Rosario MaggistroDepartment of Mathematics, University of Trento, [email protected], [email protected]
CP14
Necessary Optimality Conditions for the Time ofCrisis Control Problem.
We consider a non-smooth optimal control problem wherethe cost functional represents the time of crisis, that is, thetime spent by a solution of a control system outside a givenset. A regularization scheme of the problem based on theMoreau-Yosida approximation is proposed. We prove theconvergence of an optimal sequence for the approximatedproblem to an optimal solution of the original one. Wederive optimality conditions on the original and regularizedproblem.
Terence BayenUniversity of [email protected]
Alain Rapaport
CT15 Abstracts 65
CP14
Optimal Control Methods for Solving Laser Param-eter Extraction Problem
There are a wide range of applications involving laser prop-agation through a scattering medium. Very often, a mea-surement of the scattered light will be taken with the intentof learning some information about the medium. On thecontrary, the present work seeks to extract a description ofthe source of light and its location. A phenomenologicalmodel for off-axis intensity is presented which employs aMie scattering aerosol database. The model is extended topredict the off-axis polarized light described by the Stokesvector. Several inversion techniques are given and analyzedas well as example problems detailed which can recover therange, direction, power and polarization of the laser source.Current work on solving off-axis laser detection problemas an optimal control problem for the Radiative TransferEquation is also discussed.
Vaibhav KukrejaNaval Postgraduate [email protected]
CP14
New Sufficient Condition for the Proto-LipschitzContinuity of the State Constrained Bilateral Min-imal Time Function
We provide a sufficient condition for the proto-Lipschitzcontinuity of the state constrained bilateral minimal timefunction. Compared with the sufficient conditions givenin C. Nour and R. J. Stern, The state constrained bilat-eral minimal time function, Nonlinear Anal., 69, no. 10,3549-3558, (2008), our new condition does not impose anygeometric assumption on the constraint set S and does notinvolve points exterior to S.
Chadi NourLebanese American UniversityDepartment of Computer Science and [email protected]
CP14
Eigenvalue Assignment for Systems with MultipleTime-Delays
We consider the problem of pole assignment for a lineartime invariant plant with state feedback subject to multipletime delays in the control input. For systems with a knowntime delay, we offer a parametric formula for the feedbackgain matrix that will assign a desired set of closed-loopeigenvalues to the time-delay system. We consider somewell-established pole placement methods for systems with-out delay that utilise pole placement via state feedback inorder to achieve their desired performance objective. Weexplore the extent to which their desired control perfor-mance objective may be successfully achieved for a time-delay system by placing the primary poles of the delayedsystem at the same locations as for the system withoutdelay. The role of the secondary poles of the time-delaysystem will also be investigated since they are known toaffect both the stability and performance.
Robert S. SchmidDepartment of Electrical and Electronic Engineering
University of [email protected]
CP14
Optimal Boundary Control of Process Describedby the System of Telegraph Equation
In the present paper we study the problem boundary con-trol of oscillations described by the system of telegraphequations:{
ux + Lit +Ri = 0, ix + Cvt +Gu = 0
in rectangle QT = [0 ≤ x ≤ l] × [0 ≤ t ≤ T ].Where i(x, t)-current strength, u(x− t) – voltage in a two-wire transmission line with distributed parameters: resis-tance(R),capacity(C), charge leakage(G),self-induction(L).Will be found the explicit form of boundary control
u(0, t) = μ(t), u(l, t) = 0
which transfers the system from a given initial state
u(x, 0) = φ1(x), i(x, 0) = ψ1(x)
to a given final state
u(x, T ) = φ2(x), i(x, T ) = ψ2(x)
for a predetermined period of time T. Boundary controlprovides a minimum the following energy functional
T∫0
it(0, t)ut(0, t)dt
.
Ilya SmirnovLomonosov Moscow State [email protected]
CP15
Dynamic Risk Measures for Finite-State PartiallyObservable Markov Decision Problems
We provide a theory of time-consistent dynamic risk mea-sures for finite-state partially observable Markov decisionproblems. By employing our new concept of stochastic con-ditional time consistency, we show that such dynamic riskmeasures have a special structure, given by transition riskmappings as risk measures on the space of functionals onthe observable state space only. Moreover, these mappingsenjoy a strong law invariance property.
Jingnan Fan, Andrzej RuszczynskiRutgers [email protected], [email protected]
CP15
The Sakawa-Shindo Algorithm in Stochastic Con-trol
In this work, J.F. Bonnans, J. Gianatti and F.J. Silva. TheSakawa-Shindo Algorithm in stochastic control. Preprint,to appear, we study the extension to the stochastic caseof a first order algorithm for solving deterministic optimalcontrol problems proposed by Y. Sakawa and Y. Shindo.On global convergence of an algorithm for optimal control.IEEE Trans Aut. Control. vAC-25. 1149, 1980, and ana-lyzed in J.F. Bonnans. On an algorithm for optimal control
66 CT15 Abstracts
using Pontryagin’s maximum principle. SIAM J. Controland Optimization, 24, 1986. We need to assume that eitherthe cost functional is Lipschitz and the volatility term isnot controlled, or that the dynamics is an affine function ofthe state and the control. We prove that the iterates of thealgorithm are well defined and the cost function decreases.Moreover, for convex problems we obtain the convergenceof the iterates in the weak topology.
Francisco Jose Silva AlvarezXLIM, Universite de LimogesUniversite de [email protected]
Frederic BonnansInria-Saclay and CMAP, Ecole [email protected]
Justina GianattiOPTyCON, Universidad Nacional de [email protected]
CP15
An (s, s, S) Optimal Maintenance Policy for Sys-tems Subject to Shocks and Progressive Deterio-ration
We define a model of a system that deteriorates as a resultof (i) shocks, modeled as a compound Poisson process and(ii) deterministic, state dependent progressive rate, withvariable and fixed maintenance cost. We define mainte-nance strategies based on an impulse control model wheretime and size of interventions are executed according thesystem state. We characterize the value function as theunique viscosity solution of the HJB equation and provethat an (s, s, S) policy is optimal. We also provide numer-ical examples. Finally, a singular control problem is pro-posed where there is no fixed cost, which study and relationwith the former problem is open for future discussion.
Mauricio JuncaUniversidad de los [email protected]
CP15
Two End Points Boundary Value Problems onStochastic Optimal Transportation and Fokker-Planck Equation
We give a sufficient condition under which stochastic op-timal transportation problem is finite, by the finiteness ofthe supremum in the duality theorem, which implies theexistence of a semimartingale with given initial and termi-nal distributions. It also gives a new approach for h-pathprocesses with given initial and terminal distributions. Wealso consider the similar problem to above for a class of op-timal control problems for a family of solutions to Fokker-Planck equations.
Toshio MikamiTsuda [email protected]
CP15
An Application of Functional Ito’s Formula toStochastic Portfolio Optimization with Bounded
Memory
We consider a stochastic portfolio optimization model inwhich the returns of risky asset depend on its past per-formance. The price of the risky asset is described by astochastic delay differential equation. The investor’s goalis to maximize the expected discounted utility by choos-ing optimal investment and consumption as controls. Weuse the functional Ito’s formula to derived the associatedHamilton-Jacobi-Bellman equation. For logarithmic andexponential utility functions, we can obtain explicit solu-tions in a finite dimensional space.
Tao PangDepartment of MathematicsNorth Carolina State [email protected]
Azmat HussainOperations ResearchNorth Carolina State [email protected]
CP15
Zubov’s Method for Controlled Diffusions withState Constraints
We consider a controlled stochastic system in presence ofstate-constraints. Under the assumption of exponentialstabilizability of the system near a target set, we aim tocharacterize the set of points which can be asymptoticallydriven by an admissible control to the target with positiveprobability. We show that this set can be characterized asa level set of the optimal value function of a suitable un-constrained optimal control problem which in turn is theunique viscosity solution of a second order PDE which canthus be interpreted as a generalized Zubov equation.
Athena PicarelliDipartimento di Matematica, SAPIENZA, Universita’ [email protected]
Lars GruneMathematical InstituteUniversitaet [email protected]
CP16
Resolution-Directed Optimization-Based Dis-tributed Sensing
In this paper we study the problem of optimal zone cov-erage, using distributed sensing, i.e., a group of collabo-rating sensors. We formulate the problem as an optimiza-tion problem with time-varying cost function. We examinethe case where a group of elevated imaging sensors lookdown to and form the map of a 2-dimensional environ-ment at a pre-specified resolution. The sensors solve anoptimization problem that attempts to optimize a time-varying cost function. The cost at any time instance mea-sures the distance between the desired resolution functionand the achieved resolution until the previous time instant.We discuss the numerical implementation challenges of thisapproach and demonstrate its performance on a numericalexample.
Richard VaccaroUniversity of Rhode Island
CT15 Abstracts 67
Petros Boufounos, Mouhacine BenosmanMitsubishi Electric Research [email protected], m [email protected]
CP16
A Localized Proper Symplectic DecompositionTechnique for Model Reduction of ParameterizedHamiltonian Systems
Recently, a symplectic model reduction technique,proper symplectic decomposition (PSD), is proposed toachieve computational savings for a large-scale Hamil-tonian system while preserving the symplectic structure[arXiv:1407.6118]. As an empirical approach, PSD pre-serves system energy and stability, thus, PSD is bettersuited than the classical POD for model reduction. In thistalk, we combine PSD with the idea of parameter domainpartition, and propose a localized PSD technique for modelreduction of parameterized Hamiltonian systems.
Liqian Peng, Kamran MohseniUniversity of Florida, Gainesville, [email protected], [email protected]
CP16
Numerical Analysis of a Family of Optimal Dis-tributed Control Problems Governed by An Ellip-tic Variational Inequality
The numerical analysis of a family of distributed optimalcontrol problems governed by elliptic variational inequali-ties (for each α > 0) is obtained through the finite elementmethod when its parameter h → 0. We also obtain thelimit of the discrete optimal solutions when α → ∞ (foreach h > 0) and a commutative diagram for two continu-ous and two discrete optimal solutions are obtained whenh→ 0 and α→ ∞.
Domingo A. TarziaCONICET - Univ. AustralDepto [email protected]
Mariela OlguinUniv. Nac. de [email protected]
CP16
Uniform Boundary Observability for PolynomialApproximations of the Wave Equation
The boundary observability of the second order wave equa-tion is not preserved uniformly with respect to the dis-cretization parameter after application of classical approx-imation methods like finite differences, finite elements orspectral elements. Here we consider a spectral Legendre-Galerkin (polynomial) space-discretization of the 1-d waveequation. We show that the uniform observability can berecovered using spectral filtering, mixed formulations or aweak imposition of the boundary conditions.
Jose M. UrquizaCentre de Recherches MathematiquesUniversite de [email protected]
Ludovick GagnonUniversite Paris [email protected]
CP16
Identification of Optimum Parameters in Mathe-matical Model of Temperature Measuring Device
We propose the mathematical model describing the depen-dence of the temperature on the resistances for self-test oftemperature transducer, which is represented as system ofequation with unknown degrees and coefficients. Methodto identification of unknown parameters based on regular-ization technique is proposed. We obtain the error esti-mates of the solutions to this problem which allows to cal-culate the temperature values with guaranteed accuracyand to develop the criteria to self-test of device.
Natalia M. Yaparova, Aleksandr Shestakov
South Ural State University (National ResearchUniversity)[email protected], [email protected]
CP16
An Application of Global Sensitivity Analysis toLarge Scale Power System Small Signal Stability
We propose an application of the variance-based globalsensitivity analysis to determine impact of variation of se-lected parameters and their interactions on power systemsmall-signal stability. In practice, such analysis becomesessential when studying impact of increased penetration ofrenewable energy sources on stability. Computation is per-formed via Tensor-Train cross interpolation to map high-dimensional parameter space to system eigenvalues. Foreach interpolation point, eigenvalues are computed usingsmall-signal stability software commonly used in industry.
Rastko ZivanovicThe University of [email protected]
CP17
Approximate Controllability of a Second-OrderNeutral Stochastic Differential Equation with StateDependent Delay
In this paper the conditions for approximate controllabil-ity are investigated for a distributed second order neutralstochastic differential system with respect to the approxi-mate controllability of the corresponding linear system ina Hilbert space X. Our hypothesis is described as a ge-ometrical relation in L2(0, T : X) between the range ofthe operator B and the subspace N⊥ related with the sinefunction S(t). Thereby, we remove the need to assumethe invertibility of a controllability operator, which fails toexist in infinite dimensional spaces if the associated semi-group is compact. Our approach also removes the need tocheck the invertibility of the controllability Gramian oper-ator and the associated limit condition, which are practi-cally difficult to verify and apply. An example is providedto illustrate the presented theory. Specifically we study thefollowing second order equations modelled in the form
d(x′(t) + g(t, xt)) = [Ax(t) + f(t, xρ(t,xt)) +Bu(t)]dt
+ G(t, xt)dW (t), a.e. on t ∈ J = [0, a]
x0 = φ ∈ B, x′(0) = ψ ∈ X (1)
68 CT15 Abstracts
where A is the infinitesimal generator of a strongly con-tinuous cosine family {C(t) : t ∈ R} of bounded linearoperators on a Hilbert space X. The state space x(t) ∈ Xand the control u(t) ∈ LF
2 (J, U), where X and U are sepa-rable Hilbert spaces and d is the stochastic differentiation.Let (Ω,F , P ) be a probability space together with a nor-mal filtration Ft, t ≥ 0. Let K be a separable Hilbert spaceand {W (t)}t≥0 is a given K− valued Brownian motion orWiener process with finite trace nuclear covariance opera-tor Q > 0. The functions f, g : J ×B → X are measurablemappings in X norm and G : J × B → LQ(K,X) is ameasurable mapping in LQ(J,X) norm.
Sanjukta DasIndian Institute of Technology, Roorkee,sanjukta [email protected]
Dwijendra PandeyIndian Institute of Technology, [email protected]
CP17
Resolving the Pattern of Akt Activation by Varia-tional Parameter Estimation
Ordinary differential equation models have become one ofthe pillars for understanding complex biological systems.The equations typically contain many unknown parameterssuch as reaction rates and initial conditions, but also inputfunctions driving the system. Both are a priori unknownand need to be estimated from experimental data. Here,we introduce variational calculus and adjoint sensitivitiesto apply it for input- and parameter estimation in mam-malian target of rapamycin (mTOR) signaling. Whereasthe direct identification and quantification of different ac-tive mTOR complexes is only possible by highly challeng-ing experiments, the mathematical framework allows toreconstruct its dynamics by solving an appropriate Euler-Lagrange equation. The inherently large search space un-derlying this approach allows to test specific biological hy-potheses about the activation of protein kinase B (AKT)by mTORC2 and to reject an alternative model with highstatistical power.
Daniel KaschekInstitute of Physics, University of [email protected]
CP17
Polynomial Approximations and Controllability ofTime-Invariant Linear Ensemble Systems
Robust manipulation of an ensemble of structurally identi-cal dynamical systems is imperative for wide-ranging appli-cations from quantum control to neuroscience. We studyensemble control of finite-dimensional time-invariant lin-ear systems and develop explicit ensemble controllabilityconditions. Our derivation is based on the notion of poly-nomial approximation and the spectra properties of thesystem matrices. Practical examples and numerical sim-ulations for optimal control of such ensemble systems arepresented to demonstrate the applicability of the theoreti-cal results.
Jr-Shin LiWashington University in St. Louis
CP17
Continuous-Discrete Observers for Time-VaryingNonlinear Systems: A Tutorial on Recent Results
Continuous-discrete systems occur when the plant stateevolves in continuous time but where the output valuesare only available at discrete time instants. Continuous-discrete observers have the valuable property that the ob-servation error between the true state of the system andthe observer state converges to zero in a uniform way. Thedesign of continuous-discrete observers can often be doneby building framers, which provide componentwise upperand lower bounds for the plant state. This paper is a tuto-rial on these approaches, highlighting recent results in theliterature, and also providing previously unpublished, orig-inal results which are not being simultaneously submittedelsewhere.
Frederic [email protected]
Vincent AndrieuLAGEP-UMR 5007 Laboratory, Lyon, [email protected]
Michael MalisoffLouisiana State UniversityDepartment of [email protected]
CP17
Exact Null Controllability of Evolution Equationsby Smooth Scalar Controls and Applications toControllability of Interconnected Systems
The most of papers devoted to controllability problemsare mainly considering square integrable or piecewise-continuous controls as a set of admissible controls. How-ever some mechanical systems, for example, cars or air-crafts, require smooth controls. Exact null-controllabilityconditions for abstract linear control equations in the classof smooth controls are presented. One of applications ofthese results is the exact null-controllability conditions fora series of interconnected equations, governed by a controlof the last one. These conditions allow us to use the pre-sented abstract approach for a series contained equationsof a different structure. For example, the first one may bea parabolic control equation, and the second one may be alinear differential control system with delays, governed byscalar control, and so on. The exact null-controllability forinterconnected heat–wave equations is considered as illus-trative example.
Benzion ShklyarHolon Academic Institute of Technology,Holon, Israelshk [email protected]
CP17
Approximate Controllability of Semilinear Frac-tional Control Systems of Order α ∈ (1, 2]
The objective of this paper is to present some sufficientconditions for approximate controllability of semilinear de-lay control systems of fractional order α ∈ (1, 2] . The
CT15 Abstracts 69
results are obtained by the theory of strongly continuousα-order cosine family and sequential approach under thenatural assumption that the linear system is approximatecontrollable. At the end, an example is given to illustratethe theory.
Anurag Shukla, N Sukavanam, D.N. PandeyIIT [email protected], [email protected],[email protected]
CP18
On the Finite-Time Stabilization of Strings Con-nected by Point Mass
In this paper, the problem of finite-time boundary stabi-lization of two strings connected by point mass is investi-gated. Based on the so-called Riemann invariant trans-formation, the vibrating strings are transformed in twohybrid-hyperbolic systems, and leads to the posedness ofour system. In order to act in the system, it is desirable tochoose boundary feedbacks, in this case, Holderien stabi-lizing feedback laws to vanish in finite-time the right andthe left of the solutions are considered.
Chaker JammaziEcole Polytechnique de [email protected]
Ghada Ben BelgacemEcole Polytechnique de Tunisie, Universite de [email protected]
CP18
Metzler Matrix Transform Determination Using aNonsmooth Optimization Technique with An Ap-plication to Interval Observers
The paper deals with the design of cooperative observerswhich formulates as computing a state coordinate trans-form such that the resulting observer dynamics are bothstable and cooperative. The design of cooperative ob-servers is a key problem to determine interval observers.Solutions are provided in the literature to transform anysystem into a cooperative system. A novel approach is pro-posed which reformulates into a stabilization problem. Asolution is found using nonsmooth optimization techniques.
Emmanuel ChambonOnera - Centre de [email protected]
Pierre [email protected]
Laurent BurlionOnera - Centre de [email protected]
CP18
Delay-Independent Closed-Loop Stabilization ofNeutral Systems with Infinite Delay
Abstract: In this paper, the problem of stability and stabi-
lization for neutral delay-differential systems with infinitedelay is investigated. Using Lyapunov method, new suf-ficient condition for the stability of neutral systems withinfinite delay is obtained in terms of linear matrix inequal-ity (LMI). Memory-less state feedback controllers are thendesigned for the stabilization of the system using the fea-sible solution of the resulting LMI, which are easily solvedusing any optimization algorithms. Numerical examplesare given to illustrate the results of the proposed methods.
Iyai Davies
Control Theory and Application Centre (CTAC),[email protected]
Olivier HaasCoventry [email protected]
CP18
Observer Based Control for a Class of CoupledParabolic Hyperbolic Systems
This paper investigates the control problem for nonlinear-coupled partial differential equations that describeradiative-conductive heat transfer systems. Thanks to thespecial structure of the obtained state system, using theGalerkin method for the semi-discretization of PDE and tothe differential mean value theorem, a new linear matrixinequality condition is provided for the observer-based con-troller design. The observer and controller gain are com-puted simultaneously by solving LMI, i.e a convex problem.Also we provide a reduced order observer based controllerthat assures global asymptotic stability.
Mohamed GhattassiIECL-University of [email protected]
Mohamed BoutayebUniversity of [email protected]
CP18
On Some System-Theoretic Properties of Hamilto-nian Systems Defined on Contact Manifolds
The intrinsic description of open irreversible thermody-namic systems has given rise to the definition of controlHamiltonian systems defined on contact manifolds whichhas been call input-output contact systems. In this com-munication, we shall analyze some system-theoretic prop-erties of such systems. We shall, in particular, analyze thestructure preserving feedback of these systems, character-ize a class of contact forms achievable in closed-loop andconsider the stabilization of thse systems.
Bernhard M. MaschkeLAGEP, Universite Lyon 1, Universite de Lyon, [email protected]
CP18
Lyapunov-Razumikhin Methods for Stabilizationin the Sample-and-Hold Sense of Retarded Non-linear Systems
A new methodology for the design of stabilizers in thesample-and-hold sense for nonlinear retarded systems is
70 CT15 Abstracts
provided. It is shown that, if there exist a controlLyapunov- Razumikhin function and an induced steep-est descent state feedback, uniformly in time bounded onbounded subsets of the state space, then such feedback,applied by suitably fast sampling and holding, guaranteespractical semiglobal stability, with arbitrary small final tar-get ball of the origin.
Pierdomenico PepeUniversity of L’[email protected]
CP19
A Certified Reduced Basis Approach forParametrized Linear-Quadratic Optimal Con-trol Problems with Control Constraints
We focus at a parameter dependent PDE constrained Op-timal Control Problem with two-sided control constraints.For that problem we derive a model order reduction tech-nique that not only is capable of reducing the optimalityconditions of the problem but also the control constraints.The reduction ensures the strict feasibility for one of thetwo-sided control constraints and enables us to computean approximation and its error bound independently of theoriginal dimension of the problem.
Eduard BaderGraduate School AICESRWTH Aachen [email protected]
Mark Kaercher, Martin GreplRWTH Aachen [email protected],[email protected]
Karen VeroyAICESRWTH Aachen [email protected]
CP19
Maximum Principle for Optimal Control Prob-lems with Integral Equations Subject to State andMixed Constraints
We consider an optimal control problem with a Volterratype integral equation subject to endpoint equality and in-equality constraints, mixed state-control constraints of in-equality and equality type, and pure state inequality con-straints. The gradients of active mixed constraints withrespect to the control are assumed to be linear–positivelyindependent. We prove necessary optimality conditionswhich generalize Maximum Principle for similar problemswith ODEs. The proof is based on an extension of the con-trol system by introducing sliding mode controls and usinga relaxation theorem that allows one to approximate solu-tions of the extended system by solutions of the originalsystem. We thus obtain a family of optimal control prob-lems with extended systems, for each of which we apply thestationarity condition (Euler–Lagrange equation, obtainedearlier in our joint work with N.P. Osmolovskii), and thencompress these conditions into a universal condition thathas the form of MP.
Andrei V. DmitrukCentral Economics & Mathematics Institute,Russian Academy of Sciences
CP19
On-Line Model Predictive Control for ConstrainedImage Based Visual Servoing of a Manipulator
This paper presents an on–line image based visual servo-ing (IBVS) controller subject to the constraints based onthe robust model predictive control (RMPC) method. Acontroller is designed for the robotic visual servoing sys-tem subject to input and output constraints, such as robotphysical limitations and visibility constraints. To verifythe effectiveness of the proposed algorithm, real-time ex-perimental results on a 6 Degrees-of-Freedom robot ma-nipulator with eye-in-hand configuration are presented anddiscussed.
Amir HajilooDepartment of Mechanical and Industrial Engineering,Concordia University, Montreal, QC, [email protected]
Mohammad Keshmiri, Wen-Fang XieDepartment of Mechanical and Industrial EngineeringConcordia University, Montreal, QC, [email protected],[email protected]
CP19
Analysis of Floating Offshore Wind Turbine ModelConsidering Gyro Moment
A floating offshore wind turbine system is analyzed. Firstwe develop the floating offshore wind turbine model and theprovide analysis for the dynamics considering the gyro mo-ment based on the multi-body dynamics analysis. Specif-ically, regarding the blade pitch angle of the rotor as thecontrol input, we derive control laws for the power outputregulation, floating sway suppression, and gyro-momentsuppression at the same time. Furthermore, we providenumerical simulation to show tradeoff relationship betweenfloating sway suppression and gyro-moment suppression.
Tomohisa Hayakawa, Ryo AotaTokyo Institute of [email protected], [email protected]
CP19
Flat Systems of Minimal Differential Weight: Com-parison Between the Two-Input and the Multi-Input Case
We study flatness of control-affine systems, defined on an n-dimensional state-space. In [F. Nicolau and W. Respondek,Flatness of two-inputs control-affine systems linearizablevia one-fold prolongation, Nolcos 2013], [F. Nicolau andW. Respondek, Multi-Input Control-Affine Systems Lin-earizable via One-Fold Prolongation and Their Flatness,CDC 2013], we gave a complete geometric characterizationof systems that become static feedback linearizable after aone-fold prolongation of a suitably chosen control. Theyform a particular class of flat systems, that is of differen-tial weight n+m+ 1, where m is the number of controls.We distinguished the two-input case, i.e., m = 2 and themulti-input case, i.e., m ≥ 3. They have slightly differentgeometries and have to be treated separately. The aim of
CT15 Abstracts 71
this talk is to give a comparison between these two cases.
Florentina Nicolau, Witold RespondekINSA [email protected], [email protected]
CP19
Tracking Control of An Underactuated Au-tonomous Ship
In this paper, we will construct a control that forces po-sition and orientation of the underactuated autonomousship moves according to a reference feasible trajectory. Toachieve this objective, we use as a design tool of inputs theBacktepping methodology and Lyapunov function. Exper-imental results are given to show the tracking performance.we will illustrate trajectories with time varying velocity (si-nusoidal path). Then, we will test the tracking robustnessin presence of drag forces disturbances.
Sarra Samaali, Azgal AbichouLIM, Ecole Polytechnique de Tunisie B.P. 743 - 2078 [email protected], [email protected]
CP20
HJB Approach to Dynamic Mean-VarianceStochastic Control
We consider a general continuous mean-variance problemwhere the cost functional has an integral and a terminal-time component. We transform the problem into a super-position of a static and a dynamic optimization problem.The value function of the latter can be considered as thesolution to a degenerate HJB equation either in viscosityor in Sobolev sense (after regularization) under suitableassumptions and with implications with regards to the op-timality of strategies.
Georgios Aivaliotis, Alexander VeretennikovUniversity of [email protected], [email protected]
CP20
On Using Spectral Graph Theory to Infer theStructure of Multiscale Markov Processes
Multiscale Markov processes are used to model and controlstochastic dynamics across different scales in many appli-cations areas such as electrical engineering, finance, andmaterial science. A commonly used mathematical repre-sentation that captures multiscale stochastic dynamics isthat of singularly perturbed Markov processes. Dimen-sionality reductions techniques for this class of stochasticoptimal control problems have been studied for many years.However, it is typically assumed that the structure of per-turbed process and its dynamics are known. In this paper,we show how to infer the structure of a singularly per-turbed Markov process from data. We propose a measureof similarity for the different states of the Markov processand then use techniques from spectral graph theory to showthat the perturbed structure can be obtained by looking atthe spectrum of a graph defined on the proposed similaritymatrix.
Panos Parpas, Chin Pang HoImperial College London
[email protected], [email protected]
CP20
Robust Optimal Control for Pdes with Uncertaintyin Its Input Data
We shall review on recent results obtained by the authors([Martınez-Kessler-Periago, Robust optimal shape designfor an elliptic PDE with uncertainty in its input data, toappear in ESAIM:COCV (2015)] and [Munch-Martınez-Kessler-Periago, in preparation]) concerning robust opti-mal control problems for elliptic and parabolic partial dif-ferential equations with uncertainty in its input data. Ro-bustness is modelled by including the variance (and semi-variance) of the physical quantity to be optimized in thecost functional. For the numerical resolution of the prob-lems, the adjoint method is used. Both the direct andadjoint (non-local in the probabilistic space) equations aresolved by using a sparse grid stochastic collocation method.A number of numerical experiments in 2D will illustrate thetheoretical results and will show the computational issueswhich arise when uncertainty is quantified through randomfields.
Francisco Periago, Mathieu Kessler, Jess Martınez-FrutosUniversidad Politecnica de [email protected], [email protected],[email protected]
Arnaud MunchUniversite [email protected]
CP20
Application of Sufficient Optimality Conditions inAnalysis of Stochastic Models of Illiquid Markets
The purpose of this work is to study the optimal controlproblem of an agent in the market with random trade de-lays. In this article we present a stylized model of optimalsaving and purchases of durable goods in which the mo-ments of time when an agent makes purchases are randomand are described by Poisson flow. We find the optimalbehavior of the agent using the sufficient optimality con-ditions. We prove existence of the solution. In the case ofhigh intensity of the random process of trade the explicitform of optimal strategy is presented.
Aleksandra A. ZhukovaComputing Center of RASDivision of mathematical modelling of [email protected]
Igor PospelovComputing Center of RASna
CP21
Towards a Minimum L2-Norm Exact Control of thePauli Equation
A computational framework for the exact-control of themagnetic state and the spin of an electron is presented. Theevolution of this quantum system is governed by the Pauliequation, that is a system of Schrodinger equations coupledby the action of magnetic fields. The magnetic fields areused as controls in order to steer the quantum system froman initial state to a desired target state at a given final
72 CT15 Abstracts
time. This control framework is based on a minimum normoptimization formulation of exact-controllability quantumproblems, that allows the application of efficient Krylov-Newton optimization techniques. Furthermore, in order toprovide this framework with an adequate initialization, acontinuation procedure is discussed. Results of numericalexperiments demonstrate the effectiveness of the proposedframework.
Gabriele CiaramellaUniversity of [email protected]
CP21
Optimal Control Via Occupation Measures and In-terval Analysis
In this lecture, we present a method based on occupationmeasures to compute a guaranteed lower bound to an opti-mal control problem. Following Vinter approach, the opti-mal control problem is formulate into a linear program-ming problem of infinite dimension. Thank to Intervalarithmetic, this linear programming problem can be ap-proximate, in a reliable way. Finally, its solution gives alower bound to the optimal cost. Examples will illustratethe principle of the methodology.
Nicolas C. DelanoueLarisUniversite d’[email protected]
Sebastien Lagrange, Mehdi LhommeauLaris Universite d’[email protected],[email protected]
CP21
On Approximate Solution of Mobile (scanning)Control Problems
We describe an approximate technique for solving the so-called mobile control problems. The method is based onthe Bubnov-Galerkin procedure and allows to reduce thecontrol problem to a finite-dimensional nonlinear systemof integral constraints of equality type. An efficient nu-merical scheme is described reducing the solution of thenonlinear system to a problem of nonlinear programming.The proposed method is described for nonlinear equationswith linear boundary conditions. Two particular problemsof heating by a moving source and vibration damping by amoving absorber are considered. The system of necessaryand sufficient conditions for controllability are obtained inboth cases. Main points of numerical implementations arediscussed.
Asatur KhurshudyanYerevan State [email protected]
CP21
Towards Optimal Feedback Control of the WaveEquation Using Adaptive Sparse Grids
An approach to solve optimal feedback control problemsfor the wave equation using adaptive sparse grids is con-sidered. A semi-discrete optimal control problem is intro-duced and the feedback control is derived from the corre-
sponding value function. The value function can be charac-terized as the solution of a Hamilton-Jacobi Bellman (HJB)equation. Besides a low dimensional semi-discretization ofthe underlying wave equation it is important to solve theHJB equation efficiently to address the curse of dimen-sionality. We propose to apply a semi-Lagrangian schemeusing spatially adaptive sparse grids. Sparse grids allowthe discretization of the high(er) dimensional value func-tions arising in the numerical scheme since the curse of di-mensionality of full grid methods arises to a much smallerextent. Several numerical examples are presented. This isjoint work with J. Garcke (University of Bonn).
Axel KroenerINRIA Saclay and CMAP, Ecole [email protected]
CP21
Optimal Motion Planning for Multi-Agent Systemswith Uncertainty
Using a computational optimal control approach, a scalableparallel algorithm is developed for optimal motion plan-ning involving a large number of interacting heterogeneousagents under uncertainty. The algorithm is tested on de-signing trajectories of multiple vehicles collectively defend-ing a high-value-unit from hundreds of uncertain attackers.Simulation results demonstrate the efficiency and general-ity of the algorithm for different initial formations, and un-der different probability distributions for uncertainty. Ex-tension of the interacting scenarios utilizing Monte Carloand Quasi Monte Carlo simulations are discussed.
Panos Lambrianides, Claire Walton, Qi GongUniversity of California, Santa [email protected], [email protected],[email protected]
CP21
Fast EM Clustering For Large Data Using an In-tegrated Approach Rough-Fuzzy Granulation AndFisher Discriminate Analysis
A new fast EM clustering methodology is introduced, basedon a combined rough-fuzzy granulation and fisher discrim-inate analysis (FDA). The proposed algorithm is suitablefor mining data sets, which are large both in dimension andsize, in case generation. It utilizes FDA specification andan granular computing method for obtaining crude initialvalues of the parameters of the mixture of Gaussians usedto model the data . Rough set theory is used for featureextraction and solving superfluous attributes issue. Upperand lower approximations of rough set is calculated basedon fuzzy membership functions. Features of a pattern canhence be described in terms of three fuzzy membership val-ues in the linguistic property sets as low (L), medium (M)and high (H). FDA provides an optimal lower dimensionalrepresentation in terms of discriminating among classes ofdata.
Hesam [email protected]
Alireza YazdizadehDepartment of Electrical EngineeringShahid Abbaspour University
CT15 Abstracts 73
CP22
Distributed Controllability of the Wave EquationUsing Moving Controls
This talk aims to address the inner controllability of theone dimensional wave equation using controls with sup-ports which may vary with respect to the time variable.Theoretical and numerical aspects are considered. A gen-eralized observability inequality for the homogeneous waveequation is proven and this implies the well-posedness of amixed formulation that characterizes the controls of min-imal L2 norm. A numerical approximation of this formu-lation is presented and several numerical experiments arereported.
Nicolae CindeaUniversite Blaise Pascal, [email protected]
Carlos CastroUniversidad Politecnica de [email protected]
Arnaud MunchUniversite Blaise [email protected]
CP22
Lpv Control of a Water Delivery Canal with Re-duced Complexity Models
The problem of designing a LPV controller for a water de-livery canal using models with a priori imposed order thatapproximate plant dynamics is addressed. A water deliverycanal is an infinite dynamical system that is modelled bythe Saint-Venant equations, a pair of hyperbolic partial dif-ferential equations that embed mass and momentum con-servation for one-dimensional shallow water streams. Usinga method based on the Laplace transform, these equationsare approximated by a finite dimensional system with a pri-ori imposed order. The fact that the linear approximationrelies on a physical description of the plant allows the quan-tification of the model uncertainty in terms of the physicalparameters and the order. An LPV controller based onH∞ control is then designed. This work extends recentresults of other authors for LPV based on PID laws andthe Muskingum model, by allowing the controller order tobe imposed and by providing a direct link with physicalparameters.
Joao M. LemosINESC-ID, University of [email protected]
Daniela CaiadoINESC-ID, Univ. Lisbon, [email protected]
Jose IgrejaINESC-ID, ISEL/IPL, Lisbon, [email protected]
CP22
Predetermined Time Constant Approximation for
Model Identification Search Space Boundary byStandard Genetic Algorithm
A new predetermined time constant approximation (Tsp)method for optimising the search space boundaries for anoptimal model is proposed and presented. Using the dy-namic response period and desired settling time offered abetter suggestion for initial Tsp values of the transfer func-tion coefficients. Furthermore, an extension on boundariesderived from the initial Tsp values and the consecutive ex-ecution, brought the elite groups within feasible boundaryregions for better exploration. This enhanced the locatingof the optimal values of time constant for identified transferfunction. The Tsp method is investigated on two processes;raw data of excess oxygen and a third order transfer func-tion model with and without random disturbance. Thesimulation results assured the Tsp methods effectivenessand flexibility in assisting SGAs to find optimal transferfunction model parameters in their explorations.
Kumaran RajarathinamLiverpool John Moores [email protected]
Barry Gomm, Dingli Yu, ahmed Saad [email protected], [email protected],[email protected]
CP22
Approximate Optimal Control in Feedback Formfor Parabolic System with Quickly-Oscillating Co-efficients
In this research, the optimal control in feedback form (syn-thesis) was found for linear-quadratic problem that con-sists of semi-defined performance criterion and a paraboliclumped control system with quickly-oscillating coefficients.The exact formula for the synthesis was found and itsapproximate form that lies in substitution of quickly-oscillating parameters with average and all infinite sumswith finite was justified.References: EGOROV, A. I. Optimal Control of LinearSystems. Kiev: Vishha shkola, 1988.
Alina RusinaTaras Shevchenko National University Of [email protected]
CP22
Stabilization of Positive Infinite Dimensional Sys-tems by State Feedback with Cone Constraints onthe Inputs
For positive unstable infinite-dimensional linear systems,conditions are established for positive stabilizability anda method is described for computing a positively stabi-lizing state feedback, which guarantees that the stableclosed loop dynamics are nonnegative for specific initialstates. A feedback control is designed such that the unsta-ble finite-dimensional spectrum of the dynamics generatoris replaced by the eigenvalues of the stable input dynamicsand such that the resulting input trajectory remains in anaffine cone.
Joseph J. WinkinUniversity of Namur, Department of MathematicsNamur Center for Complex Systems (naXys)[email protected]
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M. Elarbi AchhabUniversity Chouaıb Doukkali, Department ofMathematicsEl Jadida, [email protected]
CP22
Stability of the Axially Moving Kirchhoff Stringwith the Sector Boundary Feedback Control
In this study, the stability problem for the axially movingKirchhoff string with nonlinear boundary feedback controlhas been investigated. The proposed boundary control,which satisfies a sector constraint condition, is a nega-tive feedback of the transverse velocity at the right endof string. Applying the integral-type multiplier method,the absolute stability of the axially moving Kirchhoff sys-tem is established. To validate the proposed theoreticalresults, numerical simulations are expressed by the finiteelement method.
Yuhu Wu, Tielong ShenSophia [email protected], [email protected]
CP23
Convergence Analysis of Hybrid ACO/Nelder-Mead Tuning Method for PID Controller Struc-tures with Anti-Windup
A statistical analysis of the system response quality foundby Ant Colony Optimization (ACO) based algorithm withrespect to search space discretization and the ants numberis presented for tuning 4 nonlinear controller structures.The resulting sensitivity curves permit to determine ACOparameter values to initiate Nelder-Mead (NM) algorithmwhich has permitted to reduce the average computationtime by up to 7 times for an equivalent quality response ascompare to the previous ACO-NM algorithm.
Maude Josee BlondinUniversite du Quebec a [email protected]
Pierre SicardUniversite du Quebec a [email protected]
Javier Sanchis SaezUniversitat Politecnica de [email protected]
CP23
Optimal Control of Combined Chemotherapies inPhenotype-Structured Populations
We consider a system of two scalar integro-differentialequations modelling a structured population for healthyand tumor cells under the effects of cytotoxic and cyto-static drugs. After having introduced the model and anatural optimal control problem, where the drugs are thecontrols to be optimized, we give numerical and analyticalresults.
Alexander LorzLaboratoire Jacques-Louis LionsUniversite Pierre et Marie Curie - Paris [email protected]
Jean ClairambaultINRIA [email protected]
Emmanuel TrelatLaboratoire Jacques-Louis LionsUniversite Pierre et Marie Curie - Paris [email protected]
CP23
Simultaneous Null Controllability of a SemilinearSystem of Parabolic Equations
In this paper, we consider a coupled system of two semi-linear heat equations. We prove the null controllability ofthe system with a finite number of contraints on the state.First, we show the equivalence with a null controllabilityproblem with constrained control. The latter problem wassolved in a previous work, mainly thanks to a crucial ob-servability estimate. Then we use a fixed point theorem toachieve the result.
Carole Louis-RoseUniversite des [email protected]
CP23
The Ribosome Flow Model: Theory and Applica-tions
The Ribosome Flow Model (RFM) is a nonlinear modeldescribing the movement of ribosomes along the mRNAstrand. We describe the analysis of the RFM using toolsfrom systems and control theory including contraction the-ory, monotone systems theory, and convex analysis. Jointwork with Tamir Tuller (Tel Aviv University) and EduardoD. Sontag (Rutgers University).
Michael MargaliotSchool of Elec. Eng.-SystemsTel Aviv [email protected]
CP23
Studies on Epidemic Control in Structured Popu-lations with Applications to Influenza
This work focuses on the dynamics and control of epi-demics in age-structured populations over short timescales(i.e. single Influenza outbreaks). We study the impact ofcontact structure (i.e. who mixes with whom) and com-pare the results of a well known empirical study to resultsgenerated under the assumption of proportionate mixing.Finally, we use optimal control theory to identify solutionsin the presence of limited vaccine resources.
Romarie MoralesArizona State [email protected]
CP23
Adaptive Polynomial Identification and OptimalTracking Control for Nonlinear Systems
The paper proposes an adaptive polynomial identifier and arobust nonlinear optimal tracking control scheme for poly-nomial systems. The identifier approximates an uncertainnonlinear system, where its parameters are on-line adapted
CT15 Abstracts 75
using a Kalman-Bucy filter. Then, based on the identifieran optimal tracking controller is synthesized, including anintegral term to provide it robustness. The identificationand control scheme is illustrated via simulations for thecontrol of the blood glucose level in diabetic patients.
Fernando Ornelas-Tellez, Angel E. VillafuerteUniversidad Michoacana de San Nicolas de [email protected], [email protected]
CP24
Using Piecewise-Constant Congestion Taxing Pol-icy in Repeated Routing Games
We consider repeated routing games with piecewise-constant congestion taxing in which a central planner setsand announces the congestion taxes for fixed windows oftime in advance. Specifically, congestion taxes are calcu-lated using marginal congestion pricing based on the flow ofthe vehicles on each road prior to the beginning of the tax-ing window. The piecewise-constant taxing policy in moti-vated by that users or drivers may dislike fast-changingprices and that they also prefer prior knowledge of theprices. We prove that the multiplicative update rule con-verges to a socially optimal flow when using vanishing stepsizes. Considering that the algorithm cannot adapt itselfto a changing environment when using vanishing step sizes,we propose using constant step sizes in this case. Then,however, we can only prove the convergence of the dynam-ics to a neighborhood of the socially optimal flow (with itssize being of the order of the selected step size).
Farhad FarokhiDepartment of Electrical and Electronic EngineeringThe University of [email protected]
Karl JohanssonACCESS Linnaeus CenterKTH Royal Institute of [email protected]
CP24
Zero-Sum Stopping Games with Asymmetric Infor-mation
We study a model of a two-player, zero-sum, stopping gamewith asymmetric information. We assume that the payoffdepends on two continuous-time Markov chains (X, Y),where X is only observed by player 1 and Y only by player2, implying that the players have access to stopping timeswith respect to different filtrations. We show the existenceof a value in mixed stopping times and provide a varia-tional characterization for the value as a function of theinitial distribution of the Markov chains. We also provea verification theorem for optimal stopping rules in thecase where only one player has information. (preprint:http://arxiv.org/abs/1412.1412)
Christine GruenUniversity Toulouse 1- [email protected]
Fabien GensbittelUniversity Toulouse 1 -TSE
CP24
Generic Uniqueness of the Bias Vector of Mean-Payoff Zero-Sum Games
Under some ergodicity conditions, finite state space meanpayoff zero-sum games can be solved using a nonlinear fixedpoint problem, involving a vector (bias or potential), whichdetermines the optimal strategies. A basic issue is to checkwhen the bias is unique. We show that this is always thecase for generic values of the payments of the game. Wealso discuss the application of this result to the perturba-tion analysis of policy iteration.
Antoine HochartINRIA and CMAP, Ecole [email protected]
Marianne AkianINRIA Saclay–Ile-de-France and CMAP, [email protected]
Stephane GaubertINRIA-Saclay & CMAPEcole [email protected]
CP24
On Asymptotic Value for Dynamic Games withSaddle Point
We consider two-person dynamic games with zero-sum. Weinvestigate the limit of value functions of finite horizongames with long run average cost as the time horizon tendsto infinity, and the limit of value functions of discountedgames as the discount tends to zero. Under quite weak as-sumptions on the game, we prove the Uniform TauberianTheorem: existence of a uniform limit for one of the valuefunctions implies the uniform convergence of the other oneto the same limit. The key roles in the proof were played byBellmans optimality principle and the closedness of strate-gies under concatenation.
Dmitry KhlopinKrasovskii Institute of Mathematics and [email protected]
CP24
A Fractional Mean-Field Game: Existence,Uniqueness, and Fast Equilibrium Seeking Algo-rithm
In this work, we study a fractional mean-field game prob-lem given by a fractional controlled state dynamics andpayoff that measures the gap between a mean-field termand the fractional integral of the state. First, we prove thatthe problem is well-posed. Second, we show that, given themean-field term, each decision-maker has a unique mean-field response in the space of square integrable functions.We show that a mean-field equilibrium exists and proposea fast learning algorithm that converges to mean-field equi-libria.
Hamidou TembineLSS, CNRS-Supelec-Univ. Paris Sud, [email protected]
76 CT15 Abstracts
Ousmane KodioUniversite de [email protected]
CP24
A Variational Approach to Second Order MeanField Games with Density Constraints: the Sta-tionary Case
In this work we study the existence of solutions of a sta-tionary Mean Field Game (MFG) system with a densityconstraint on the distribution of the agents. We prove theexistence of a solution for both, the subquadratic and thesuperquadratic cases. Our approach is based on the inter-pretation of the MFG system as the optimality conditionof the optimal problem of a stationary Fokker-Planck equa-tion. Using tools from convex analysis and some sharp re-sults in the theory of elliptic equations with measure data,we derive first the optimality system for the qualified prob-lem, i.e. when the Slater condition for the density con-straint is satisfied. For non qualified problems, we proceedby using an approximation argument.
Francisco Jose Silva AlvarezXLIM, Universite de LimogesUniversite de [email protected]
Alpar Richard MeszarosUniversite d’Orsayalpar [email protected]
CP25
Non-Commutative Least Mean Squares Estimatorsand Coherent Observers for Linear Quantum Sys-tems
Quantum versions of control problems are often more dif-ficult than their classical counterparts. To make furtherprogress, new methods need to be devoloped to estimatethe internal state of plants. In this talk, we consider plantswhose internal states are governed by non-commutative lin-ear quantum stochastic differential equations. We obtainnon-commutative least mean squares estimators, and giveconditions which make them physically realizable. Also,some algorithms for designing coherent quantum observerswill be presented.
Nina H. AminiCNRS [email protected]
Zibo Miao, Yu PanANU College of Engineering & Computer [email protected], [email protected]
Matthew JamesFaculty of Engineering and Information TechnologyAustralian National [email protected]
Hideo MabuchiApplied Physics DepartmentStanford [email protected]
Shanon L. VuglarUniversity of New South Wales,
Australian Defence Force [email protected]
CP25
Convergence of Caratheodory Solutions for Primal-Dual Dynamics in Constrained Concave Optimiza-tion
This paper characterizes the asymptotic convergence prop-erties of the primal-dual dynamics to the solutions of aconstrained concave optimization problem using classicalnotions from stability analysis. We motivate our studyby providing an example which rules out the possibility ofemploying the invariance principle for hybrid automata toanalyze the asymptotic convergence. We understand thesolutions of the primal-dual dynamics in the Caratheodorysense and establish their existence, uniqueness, and con-tinuity with respect to the initial conditions. We employthe invariance principle for Caratheodory solutions of adiscontinuous dynamical system to show that the primal-dual optimizers are globally asymptotically stable underthe primal-dual dynamics and that each solution of thedynamics converges to an optimizer.
Ashish CherukuriUniversity of California, San [email protected]
Enrique MalladaCalifornia Institute of [email protected]
Jorge CortesDepartment of Mechanical and Aerospace EngineeringUniversity of California, San [email protected]
CP25
Analysis of Uncertain Systems to Compute TheirApproximate Models
Mathematical modelling of practical available systems re-sulted in higher order models along with the uncertaintywithin making their study and analysis difficult. As a so-lution, emerged model order reduction. An effective pro-cedure to derive a reduced model for an uncertain systemsusing Routh approximant is discussed here. The proposedmethodology is an extension of an existing technique forcontinuous-time uncertain systems. The algorithm is jus-tified and strengthened by various available examples fromthe literature.
Amit Kumar Choudhary
Indian Insttitute of Technology (Banaras HinduUniversity)[email protected]
Shyam Krishna NagarDept. of Electrical EngineeringIIT (BHU) Varanasi, U.P. [email protected]
CP25
Time Averaged and Spatial Averaged Convergencefor a Direct Coupled Distributed Coherent Quan-
CT15 Abstracts 77
tum Observer
This presentation considers the convergence properties of adistributed direct coupling quantum observer for a closedlinear quantum system. The proposed distributed observerconsists of a network of quantum harmonic oscillators andit is shown that the distributed observer converges in atime averaged sense in which each component of the ob-server estimates the specified output of the quantum plant.Simulation results also indicate that if the observer is suit-ably constructed then the spatial average of the observeroutputs will converge to the plant variable of interest on afinite time interval.
Ian PetersenUniversity of New South Wales,Australian Defence Force [email protected]
CP25
Model Calibration and Control Design in the Pres-ence of Model Discrepancy
Measurement and model errors produce uncertainty inmodel parameters estimated through least squares fits todata or Bayesian model calibration techniques. In manycases, model errors or discrepancies are neglected duringmodel calibration. However, this can yield nonphysicalparameter values for applications in which the effects ofunmodeled dynamics are significant. It can also produceprediction intervals that are inaccurate in the sense thatthey do not include the correct percentage of future ob-servations. In this presentation, we discuss techniques toquantify model discrepancy terms in a manner that yieldsphysical parameters and correct prediction intervals. Weillustrate aspects of the framework in the context of dis-tributed structural models with highly nonlinear parameterdependencies. Finally, we will discuss the impact of modeldiscrepancy and uncertainty quantification on robust con-trol design.
Ralph C. SmithNorth Carolina State UnivDept of Mathematics, [email protected]
CP25
Aircraft Preliminary Design Using Nonlinear In-verse Dynamics
The question: What shape should an aircraft have to givecertain desirable properties? An answer is given by apply-ing Nonlinear Inverse Dynamics. In general this approachis used to define flight trajectories calculations and flightcontrol systems design. Nonlinear model matching is ap-plied to obtain the preliminary design of aircraft. Given aset of customer flight specifications the parameters whichdefine the shape and size of the required aircraft are deter-mined.
Daniel L. MartınezCENTRO DE INVESTIGACIN E INNOVACINEN INGENIERA [email protected]
Eduardo Liceaga-Castro, Marco Torres-ReynaCentro de Investigacion e Innovacionen Ingeniera Aeronautica
[email protected], marco torres @hotmail.com
CP26
Extremum Seeking-Based Indirect Adaptive Con-trol for Nonlinear Systems with State-DependentUncertainties
We study in this paper the problem of adaptive trajec-tory tracking for nonlinear systems affine in the controlwith bounded state-dependent uncertainties. We proposeto use a modular approach, in the sense that we first de-sign a robust nonlinear state feedback which renders theclosed loop input to state stable (ISS) between an esti-mation error of the uncertain parameters and an outputtracking error. Next, we complement this robust ISS con-troller with a model-free multiparametric extremum seek-ing (MES) algorithm to estimate the model uncertainties.The combination of the ISS feedback and the MES algo-rithm gives an indirect adaptive controller. We show theefficiency of this approach on a two-link robot manipulatorexample.
Mouhacine BenosmanMitsubishi Electric Research Laboratoriesm [email protected]
Meng XiaUniversity of Notre [email protected]
CP26
Tracking Optimal Trajectories in the RestrictedThree-Body Problem Using Lqr Feedback
Existing literature has presented optimal trajectories in thecircular-restricted three-body problem (CRTBP) for ballis-tic capture and orbit transfers. However, there has beenonly a limited discussion thus far of how to stabilize suchtrajectories in the presence of noise; e.g. navigation er-rors, thrust resolution and misalignment. This work ad-dresses stability concerns by introducing an LQR-basedfeedback strategy that tracks an optimal trajectory in theEarth-Moon system. Stability margins are assessed usingLyapunov-based methods.
Joseph DiniusUniversity of ArizonaProgram in Applied [email protected]
CP26
Predicting Time Series Outputs and Time-to-Failure for An Aircraft Controller Using BayesianModeling
The determination of system stability and time before lossof control (time-to-failure) is important for aircraft safety.We describe a hierarchical statistical model using TreedGaussian Processes to predict stability, time-to-failure, andoutput time series. We first classify the data into successand failure, then use separate models for prediction. Abasis representation for curves allows us to model variablelength curves. We demonstrate our prediction method witha neuro-adaptive flight control system.
Yuning HeNASA Ames Research Center
78 CT15 Abstracts
CP26
Robust Regulation of Siso Systems: The FractionalIdeal Approach
We solve the robust regulation problem for single-inputsingle-output plants by using fractional ideals and with-out using coprime factorizations. We are able to formulatethe famous internal model principle in a form suitable forgeneral factorizations. By using it we are able to give anecessary and sufficient solvability condition for the robustregulation problem, which leads to a design method for arobustly regulating controller. The theory is illustrated byexamples.
Petteri LaakkonenTampere University of [email protected]
Alban Quadrat
Inria Saclay - Ile-de-France, Projet [email protected]
CP26
The Complexity of Uncertainty in Markov DecisionProcesses
We consider Markov decision processes with uncertaintransition probabilities and two optimization problems inthis context: the finite horizon problem which asks to findan optimal policy for a finite number of transitions and thepercentile optimization problem for a wide class of uncer-tain Markov decision processes which asks to find a pol-icy with the optimal probability to reach a given rewardobjective. To the best of our knowledge, unlike other op-timality criteria, the finite horizon problem has not beenconsidered for the case of bounded-parameter Markov de-cision processes, and the percentile optimization problemhas only been considered for very special cases. We es-tablish NP-hardness results for these problems by showingappropriate reductions.
Dimitri ScheftelowitschTU [email protected]
CP26
Finite Step Algorithms for the Solution of RobustControl Problems with Application to Hydraulicand Pneumatic Control Systems
In this paper a unification of robust control stabilizabil-ity algorithms solving many control problems will be pre-sented. The convergence of the algorithm is guaranteedunder solvability conditions depending upon the particu-lar robust control problem. A main algorithm with minormodifications is presented for solving many robust controlproblems of linear systems with nonlinear uncertain struc-ture, such as robust output asymptotic tracking or robustPID design. The main algorithm is based on the respectiveresults of Hurwitz invariability (robust stabilizability) ofuncertain gained controlled polynomials. The applicabilityof the proposed algorithms will be illustrated to various hy-draulic and pneumatic uncertain systems such as hydraulicpneumatic actuators, hydraulic motors and pumps. Thealgorithms will be implemented in micro controller basedplatforms and PLC platforms providing a helpful tool for
controlling many industrial processes. AcknowledgmentThis research has been co-financed by the European Union(European Social Fund ESF) and Greek national fundsthrough the Operational Program ”Education and LifelongLearning” of the National Strategic Reference Framework(NSRF) - Research Funding Program: ARCHIMEDES III.Investing in knowledge society through the European So-cial Fund. (ARCHIMEDES III-STRENGHTENING RE-SERCH GROUPS IN TECHNOLOGICAL EDUCATION,NSRF 2007-2015).
Michael G. SkarpetisSterea Ellada Institute of TechnologyDepartment of Automation [email protected]
Fotis KoumboulisSterea Ellada Institute of Technology,Department of Automation [email protected]
CP27
A Decentralized Team Routing Strategy amongTelecom Operators in an Energy-Aware Network
We consider a networking infrastructure, upon which var-ious “large” users (e.g., Telecom Operators, data centers,etc.) have multiple paths to deliver an aggregated entryflow to a certain destination. The flow of each user can besplit among the different paths that traverse energy-awarerouters. The routers adopt a specific strategy to minimizethe power–delay product for each link, which gives rise toquadratic link (in the aggregated link flows) cost functions.We seek person–by–person satisfactory (p.b.p.s.) strate-gies stemming from a team optimal control problem of theusers. The team optimization problem is defined amongDecision Makers (DMs – one for each user) that try to min-imize a common aggregate cost function of their routes,each one acting solely on the basis of the knowledge ofthe amount of flow to be routed. We derive piecewise lin-ear p.b.p.s. solutions, which are characterized by a set ofparameters. The latter can be found by solving a set ofnonlinear fixed point equations.
Franco DavoliDITEN - University of [email protected]
Michele AicardiDIBRIS-University of [email protected]
Roberto BruschiCNIT - University of Genoa Research [email protected]
Paolo LagoDITEN-University of [email protected]
CP27
Estimating the Relative Position of Mobile Agentson Jordan Curves from Ambiguous Proximity Data
We consider the problem of estimating the relative posi-tions of an ensemble of agents, moving along a Jordancurve. When two of them get sufficiently close, they canmeasure their Euclidean distance. Based on the knowl-
CT15 Abstracts 79
edge of agent dynamics, a prediction-correction algorithmdescribed is proposed to recursively estimate the relativeposition along the Jordan curve for each pair of agents. Ex-ploiting these position estimates, decentralized formationcontrol strategy can be implemented on the curve.
Franco Garofalo, Piero De Lellis, Francesco Lo Iudice,Giovanni ManciniUniversity of Naples Federico [email protected], [email protected],[email protected], [email protected]
CP27
An Inversion-Based Fault Reconstruction Ap-proach in Nonlinear Systems
This paper presents an inversion-based fault reconstructionapproach for a wide class of nonlinear systems subject toan actuator or plant fault. If the nonlinear system hasfinite relative order with respect to the fault signal, theinverse system as an observer-based filter, reproduces thefault at its output. A simulation for a continuous-stirredtank reactor (CSTR) model include flow rate fault is usedto illustrate the effectiveness of the proposed method.
Hamed KazemiShahid Beheshti University (SBU)[email protected]
Alireza YazdizadehDepartment of Electrical EngineeringShahid Abbaspour [email protected]
Abbas AliabadiMAPNA [email protected]
CP27
Image Compression and Signal Transform DesignsBased on Fast and Stable Discrete Cosine and SineTransformation Algorithms
Discrete Fourier Transformation is engaged in image pro-cessing, signal processing, speech processing, feature ex-traction, convolution etc. In this talk we elaborate imagecompression results based on stable, fast, and recursiveradix-2 Discrete Cosine Transformation (DCT) and Dis-crete Sine Transformation (DST) algorithms having sparseand orthogonal factors. We also propose signal transformdesigns constructed solely via variants of DCT and DST re-spect to decimation in time and frequency algorithms hav-ing sparse, orthogonal, rotation/rotation-reflection, andbutterfly matrices.
Sirani M. PereraDaytona State [email protected]
CP27
A Collocation Method for Zakai Equations
We propose a new numerical method for Zakai equationsin nonlinear filtering. The method constructs a numeri-cal solution by the quasi-interpolation in a recursive way.We provide the rigorous bound of the approximation er-ror defined by Sobolev norm, which is consisting of the
time-discretization errors and the interpolation ones thatare accumulated over time steps.
Yumiharu NakanoGraduate School of Innovation ManagementTokyo Institute of [email protected]
CP27
The Cauchy Attitude Estimator for PlanetaryFlyby in An Intense Radiation Background
There are many estimation problems where both impulsivemeasurement and/or process noise occurs. Handling out-liers in the data has been a heuristic process. Recently,a recursive estimator for heavy tailed Cauchy probabilitydensity functions that model the measurement and processnoise into a discrete-time linear system has been developed.This new scheme directly handles impulsive noise. In fact,for Cauchy noise, this estimator produces the conditionalmean and is thereby a minimum variance estimator. Todemonstrate the improvement that is obtained, this newestimator is applied to a planetary flyby, where the star-tracker measurements are impulsive due to the electromag-netic radiation characteristics of the planet.
Jason L. [email protected]
CP28
Metric Invariance Entropy and Conditionally In-variant Measures
A notion of measure-theoretic invariance entropy is con-structed with respect to a conditionally invariant measurefor control systems in discrete time. It is shown that themetric invariance entropy is invariant under conjugacies,the power rule holds, and the (topological) invariance en-tropy provides an upper bound.
Fritz ColoniusUniversity of [email protected]
CP28
Controlling Spatiotemporal Chaos in ActiveDissipative-Dispersive Nonlinear Systems
We develop a novel generic methodology for the sta-bilization and control of infinite-dimensional dynamicalsystems exhibiting low-dimensional spatiotemporal chaos.The methodology is exemplified with the generalizedKuramoto-Sivashinsky equation, the simplest possible pro-totype that retains that fundamental elements of any non-linear process involving wave evolution. We show that withan appropriate choice of time-dependent feedback controlswe are able to stabilize and/or control all stable or unsta-ble solutions, including steady solutions, travelling wavesand spatiotemporal chaos. We also show that the pro-posed methodology, appropriately modified, can be usedto control the stochastic Kuramoto-Sivashinsky equationand related models.
Susana N. GomesDepartment of MathematicsImperial College [email protected]
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Marc PradasDepartment of Mathematical [email protected]
Serafim KalliadasisDepartment of Chemical EngineeringImperial College [email protected]
Demetrios PapageorgiouDepartment of MathematicsImperial College London, [email protected]
Grigorios PavliotisImperial College LondonDepartment of [email protected]
CP28
Optimal Control of Passive Particles Advected byTwo-Dimensional Point Vortices
The objective of this work is to develop a mathematicalframework for the modeling, control and optimization ofdynamic control systems whose state variable is drivenby interacting ODE’s and PDE’s, which should provide asound basis for the design and control of new advanced en-gineering systems. We are applying necessary conditions ofoptimality to the two-dimensional incompressible Navier-Stokes flow, which can be reduced to a problem with ODEdynamics, by using vortex and multiprocess methods, tostudy the position of a particle subject to this flow.
Teresa D. GriloFCUP/[email protected]
Sılvio [email protected]
Fernando F. Lobo PereiraFaculadade de Engenharia da Universidade do PortoPorto, [email protected]
CP28
Optimal Control of Managed Aquifer Recharge(mar) From Infiltration Trenches With Objec-tive of Minimal Waterlogging: Revisiting thePolubarinova-Kochina and Pontryagin Legacy
In MAR, surface water infiltration perturbs water table(moving free boundary). Three phases of transient MARare analytically investigated using Green-Ampts ODE,Boussinesqs linearized PDE and Laplaces PDE with thevolume of wetted soil at a specified instance and free sur-face depth above substratum as criteria. Hydrogeologicalparameters and total annual volume of injected water areconstraints. The controls are: time schedule, filling depth-size-shape of trench, number of trenches. Optimal MARscenarios are found.
Anvar KacimovSultan Qaboos [email protected]
Ali Al-MaktoumiSultan Qaboos University, OmanDepartment of Soils, Water and Agricultural [email protected]
Vitaly ZlotnikUniversity of Nebraska-Lincoln, USADepartment of Earth and Atmospheric [email protected]
Yurii ObnosovKazan Federal University, RussiaInstitute of Mathematics and [email protected]
CP28
Subdifferential Inclusions and Tracking Problems
The evolution of the state of a system can be usually de-scribed by a differential inclusion
x′(t) ∈ F (t, x(t)). (2)
Moreover, in many systems admissible states have to sat-isfy additional viability constraints
x(t) ∈ K(t) (3)
where K(·) is a family of moving subsets (a tube). In thislecture we address a control problem that concerns (2)-(3).In fact, given an initial state x0, we are interested in findinga control u(t) such that there exits (at least) a solution of
{x′(t) ∈ u(t) + F (t, x(t))
x(0) = x0
(4)
reaching the tube K(·) at a finite time t∗ and remainingthereafter, that is, such that (3) is satisfied whenever t ≥t∗.
Jose Alberto Murillo HernandezDepartamento de Matematica Aplicada y EstadsticaUniversidad Politecnica de [email protected]
CP28
Swirling Flow Stabilisation and the KdV Equation
Asymptotic analysis of swirling flow through a pipe leadsto the Korteweg de Vries equation. We discuss what thistells us about the stability of the flow and what it suggestsabout ways to stabilise the flow.
Steve TaylorUniversity of Auckland, New [email protected]
MS1
Dynamic Programming in Mathematical Finance
Mathematical Finance has introduced new type of stochas-tic control problems. In this context, the martingalemethod has been used to solve them. This gives the im-pression that probabilistic techniques are the only way toobtain a solution. We want to show that purely analyticaltechniques can be used for the same result. Not only itis useful to have additional techniques, but also analytical
CT15 Abstracts 81
techniques allow for more constructive solutions. In par-ticular, one does not need to rely on the martingale repre-sentation theorem to construct optimal stochastic controls.We will discuss the concepts and the main techniques. Twomodels will be considered, the classical consumer-investormodel and a model describing the choice of projects foran entrepreneur. A credit risk problem will be solved inthis framework. Do not include references or citations sep-arately at the end of the abstract. Instead, all citationsmust be in text in the general form [Authorname, Title,etc]
Alain BensoussanThe University of Texas at Dallas andCity University of Hong Kong, Hong [email protected]
MS1
Optimal Control of Piecewise DeterministicMarkov Processes
The main goal of this talk is to study the infinite-horizonexpected discounted continuous-time optimal control prob-lem of piecewise deterministic Markov processes (PDMPs)with the control acting continuously on the jump intensityλ and on the transition measure Q of the process but noton the deterministic flow φ. The set of admissible controlstrategies is assumed to be formed by policies, possibly ran-domized and depending on the past-history of the process,taking values in a set valued action space. We provide suf-ficient conditions based on the three local characteristicsof the process φ, λ, Q, and the semi-continuity propertiesof the set valued action space, to guarantee the existenceand uniqueness of the integro-differential optimality equa-tion (the so called, Bellman-Hamilton-Jacobi equation) aswell as the existence of an optimal (and δ-optimal, as well)deterministic stationary control strategy for the problem.
Oswaldo CostaDepartamento de Engenharia de Telecomunicacoes eControEscola Politecnica da Universidade de Sao [email protected]
Francois DufourInstitut de Mathematiques de Bordeaux INRIA BordeauxUniversite Bordeaux [email protected]
Alexey PiunovskiyDepartment of Mathematical SciencesUniversity of [email protected]
MS1
Controlling Lvy Processes by Absolutely Continu-ous Processes
Given a spectrally negative Levy process in the real line, weconsider the problem of controlling its direction (and inten-sity) using in an additive way absolutely continuous pro-cesses, adapted to the information generated by the Levyprocess. Using the fluctuation theory of processes, it ispossible to describe the functional that we aim to minimizein terms of the scale function associated with the process,and prove that an optimal solution has a refracted form,described in terms of the frontier of some set.
Daniel Hernandez-Hernandez
Centro de Investigacion en Matematicas, Guanajuato,[email protected]
MS1
A Measure Approach for Continuous InventoryModels: Long-Term Average Criterion
This paper examines a single-item inventory process, mod-elled by a one-dimensional SDE, which incurs long-termaverage costs. The manager may increase the current in-ventory level but not reduce the inventory level. This paperprovides minimal conditions which imply that an optimalordering policy exists in the class of (s, S) processes. Thevalue is obtained over a restricted class of policies and thenshown to be optimal in general. Both linear and nonlinearoptimization is involved.
Kurt HelmesHumboldt University of [email protected]
Richard StockbridgeUniversity of Wisconsin - [email protected]
Chao ZhuUniversity of [email protected]
MS2
Reference Tracking of Depth of Anesthesia UsingOptimal Control
Optimal control theory has gained increasing importance inbiomedical applications, e.g., in the automatic administra-tion of anesthetics during general anesthesia. One exampleof a monitored state is the depth of anesthesia, which isusually achieved by the joint administration of hypnoticsand analgesics. This state is quantified by the bispectralindex (BIS) that varies between 97.7% and 0%. On theother hand, the amount of drug to be administered shouldbe optimized both for patient health and for economicalreasons. This motivates the use of optimal control in thisfield of application. In this contribution a static state-feedback control law is considered. In order to determinea suitable feedback gain, a nonlinear optimal control prob-lem (OCP) is formulated and solved using direct methods.These methods have become increasingly useful when com-puting the numerical solution of the OCP. Moreover, theyare known to provide a very robust and general approach.
Julaina Almeida, Luis Tiago PaivaUniversidade do PortoFac. Engenharia, [email protected], [email protected]
Teresa F. MendoncaUniversidade do PortoFaculdade de Ciencias, Departamento de [email protected]
Paula RochaUniversidade do PortoFac. Engenharia, Portugal
82 CT15 Abstracts
MS2
Identification of the Fragmentation Role in theAmyloid Assembling Processes and Optimizationof Current Amplification Protocols
The goal is to establish a kinetic model of amyloid for-mation which will take into account the contribution offragmentation to the de novo creation of templating in-terfaces. We propose a new, more comprehensive math-ematical model which takes into account previously ne-glected phenomena potentially occurring during the tem-plating and fragmentation processes. In particular, we tryto capture a potential effect of the topology and geome-try of prion folding on the elongation and fragmentationproperties of a polymer of a given length by separatingpolymers of the same length into several compartments.Additionally, we apply techniques from geometric controlto the new model to design optimal strategies for accelerat-ing the current amplification protocols, such as the ProteinMisfolding Cyclic Amplification (PMCA).
Monique ChybaDept. of MathematicsUniversity of Hawaii at Manoa, [email protected]
Pierre GabrielUniversite de Versailles [email protected]
Yuri MileykoDept. of Mathematics University of Hawaii at Manoa,[email protected]
Jean-Michel CoronUniversite Pierre et Marie Curie, [email protected]
Rezaei HumanInsitut National de la Recherche en Agronomie - INRA,[email protected]
MS2
Slow Invariant Manifold Reduced Models for StiffChemical Kinetics ODE in Optimal Control
Model reduction in the context of numerical optimal con-trol using a multiple shooting approach is a useful wayto decrease the computational complexity. Mathematicalmodels for chemical kinetics based on stiff ordinary differ-ential equations can often be reduced for example by us-ing a trajectory-based optimization approach to compute aslow invariant manifold within the state space. This seemsto be a profitable approach because on the one hand a op-timal control problem has to be solved and on the otherhand the model reduction is performed via optimizationas well. As an example, we discuss the Michaelis-Mentenenzyme kintetics in singularly perturbed form and demon-strate the applicability of our model reduction method forsingularly perturbed optimal control problems.
Dirk Lebiedz, Pascal F. Heiter, Marcel RehbergUlm University
[email protected], [email protected],[email protected]
MS2
On the Significance of Singular Controls in OptimalSolutions to Biomedical Problems
Optimal control problems for mathematical models ofbiomedical problems often can be described by control-affine nonlinear systems with an L1-type objective. Typi-cally the controls are bounded, for example as dose ratesor concentrations of therapeutic agents in cancer treat-ments or as vaccination rates in epidemiology. In solutions,bang-bang controls represent administrations of agents atfull dose with rest periods while singular controls typicallyare time-varying solutions at intermediate and thus lowerthan maximum dose values. There exists mounting medi-cal evidence that ”more is not necessarily better” in can-cer treatments and this has generated significant researchinterest in what could be called the biologically optimaldose (BOD). From an optimization perspective, singularcontrols stand out as the prime candidates in this con-text. Although in few problems a full synthesis of optimalcontrolled trajectories can be established, it becomes ofinterest, both theoretically and from an application pointof view, to analyze problems in which singular controlsappear as extremals. In this talk, challenges related tofinding optimal solutions, like establishing optimality ofsingular controls, bang-singular junctions and synthesis ofcontrolled trajectories will be addressed. The connectionsbetween the types of solutions and medical concepts includ-ing metronomic chemotherapy, chemo-switch protocols andadaptive therapy will be discussed.
Urszula LedzewiczSouthern Illinois University, [email protected]
Heinz SchaettlerWashington [email protected]
MS3
Minimax Solutions for First Order Mean FieldGames
We consider first order mean field game system with non-smooth Hamiltonian enjoying the sublinear growth. Pro-posed definition of minimax solution means that the graphof value function is viable under certain differential inclu-sion, when the measure on the state space is determinedby a measure on the set of viable trajectories. We provethe existence theorem, and the consistency of minimax andclassical solutions. Additionally, we construct a near-Nashequilibrium for finite-player game.
Yurii AverboukhKrasovskii Inst. of Math and MechanicsUsB [email protected]
MS3
Risk-Sensitive Optimal Control for Mean-Field Dy-namics under Partial Observation
We establish a stochastic maximum principle (SMP) forcontrol problems of partially observed diffusions of mean-
CT15 Abstracts 83
field type with risk-sensitive performance functionals.
Boualem [email protected]
Hamidou TembineLSS, CNRS-Supelec-Univ. Paris Sud, [email protected]
MS3
Mean Field Games: New Results and New Per-spectives
Abstract not available.
Olivier GueantUniversite Paris-DiderotUFR de [email protected]
MS3
Mean Field Inspection Games
In this talk we present a new model of mean field inspec-tion games with one major player and a large number ofinspectees on a discrete state space.
Wei YangUniversity of [email protected]
Vassili KolokoltsovStatistics Dept, University of [email protected]
MS4
Optimal Control of Phase Field Equations with Dy-namic Boundary Conditions
This talk deals with an optimal control problems for theAllen-Cahn equation with a nonlinear dynamic boundarycondition involving the Laplace-Beltrami operator. Thenonlinearities both in the bulk and on the boundary canbe singular, i.e., they may range from the derivative of log-arithmic potentials confined in [−1, 1] to the subdifferentialof the indicator function of the interval [−1, 1] up to a con-cave perturbation. We first examine the case of logarithmicnonlinearities: in a recent paper by Colli and Sprekels thecorresponding control problems were studied, and resultsconcerning existence and first-order necessary and second-order sufficient optimality conditions were shown. Then, inthe case of double obstacle potentials, a joint research withM. H. Farshbaf-Shaker and J. Sprekels focused on the ”deepquench” approximation (i.e., approximating the indicatorfunction by logarithmic nonlinearities) and led us to estab-lish both the existence of optimal control and first-ordernecessary optimality conditions. Extensions of these re-sults to the viscous Cahn-Hilliard and Cahn-Hilliard equa-tion with dynamic boundary condition will be outlined.
Pierluigi ColliDipartimento di Matematica ”F. Casorati’, Universita’ diPa
MS4
Optimal Control of the Cahn-Hilliard VariationalInequality
Abstract not available.
Michael HintermullerDepartment of Mathematics, Humboldt-University [email protected]
MS4
Optimal Distributed Control of Nonlocal Cahn-Hilliard/Navier-Stokes Systems in 2D
In this talk, we report on joint work with S. Frigeri and E.Rocca (both WIAS Berlin). We study the distributed op-timal control of nonlocal Cahn-Hilliard/Navier-Stokes sys-tems in the two-dimensional case under box constraints forthe controls. The nonlocal contribution to the chemicalpotential has the form of a convolution integral with anintegral kernel having certain smoothness properties; forinstance, potentials of Newton or Bessel type are admit-ted. Upon showing sufficiently strong regularity and sta-bility properties for the solutions to the state system, theFrechet differentiability of the control-to-state mapping insuitable function spaces can be established, and first-orderoptimality conditions in terms of an adjoint System and avariational inequality can be derived.
Jurgen SprekelsDepartment of Mathematics, Humboldt-Universitat [email protected]
MS4
Optimal Control of Electromagnetic Fields Gov-erned by the Full Time-Dependent Maxwell Equa-tions
In this talk, we present recent results in the optimal con-trol of the full time-dependent Maxwell equations. Ourgoal is to find an optimal current density and its time-dependent amplitude which steer the electric and mag-netic fields to the desired ones. The main difficulty ofthe optimal control problem arises from the complexity ofthe Maxwell equations, featuring a first-order hyperbolicstructure. We present a rigorous mathematical analysisfor the optimal control problem. Here, the semigroup the-ory and the Helmholtz decomposition theory are the keytools in the analysis. Our theoretical findings include ex-istence, strong regularity, and KKT theory. The corre-sponding optimality system consists of forward-backwardMaxwell equations for the optimal electromagnetic and ad-joint fields, magnetostatic saddle point equations for theoptimal current density, and a projection formula for theoptimal time-dependent amplitude. A semismooth New-ton algorithm in a function space is established for solvingthe nonlinear and nonsmooth optimality system. The pa-per is concluded by numerical results, where mixed finiteelements and Crank-Nicholson schema are used.
Irwin YouseptFakultat fur Mathematik, Universitat Duisburg-Essen
84 CT15 Abstracts
MS5
Some Results on the Stability of 1-D Nonlinear Hy-perbolic Systems on a Finite Interval
This talk deals with the control of systems modeled by hy-perbolic systems in one space dimension. These systemsappear in various real life applications (navigable riversand irrigation channels, heat exchangers, plug flow chemi-cal reactors, gas pipe lines, chromatography,...). On thesesystems we show methods to construct stabilizing feedbacklaws. We also show the importance of the choice of func-tional spaces for the stabilization issue in the nonlinearcase.
Jean-Michel CoronUniversite Pierre et Marie Curie, [email protected]
MS5
Performance Estimates for Model Predictive Con-trol of Pdes
Model Predictive Control (MPC) is a control techniquewhich synthesizes an infinite horizon control function frompieces of finite horizon optimal control functions. It canthus be seen as a model reduction technique in time. Often,the goal of MPC is to obtain a tracking control steering thesystem state to a desired reference. In this talk, we explorefor various types of PDEs how the cost functional in thefinite horizon PDE optimization in the MPC scheme mustbe chosen in order to obtain the desired tracking behaviourand good performance in the sense of an infinite horizonobjective.
Lars GruneMathematical InstituteUniversitaet [email protected]
Nils AltmullerUniversity of Bayreuth, [email protected]
MS5
Optimal Control for the Wave Equation: InfiniteVersus Finite Horizon
We consider a vibrating string that is fixed at one endwith Neumann control action at the other end. We studya problem of optimal control where the deviation from thedesired state is penalized on the whole time interval andanalyze the asymptotic properties as the time horizon tendsto infinity. Due to the structure of the objective function,most of the optimal control action is concentrated at thebeginning of the time interval.
Martin GugatInstitute of TechnologyDarmstadt, [email protected]
MS5
PBDW: Real-Time State Estimation forParametrized PDEs
We present the parametrized-background data-weak
(PBDW) formulation, a real-time and in-situ data as-similation (state estimation) framework for physical sys-tems modeled by parametrized PDEs. The formulationaddresses anticipated uncertainty through a background(prior) space associated with the parametrized PDE, in-corporates unanticipated uncertainty through a represen-tation update space, identifies stability-informed choicesof experimental observations, and incorporates elements ofmodel reduction to provide real-time computational effi-ciency. We demonstrate the effectiveness of the formula-tion using a real physical system.
Masayuki Yano, James PennMassachusetts Institute of [email protected], [email protected]
Tommaso [email protected]
Anthony T. PateraMassachusetts Institute of TechnologyDepartment of Mechanical [email protected]
Yvon MadayUniversite Pierre et Marie Curieand Brown [email protected]
MS6
Output Regulation for Linear Hybrid Systems withUnpredictable Jumps: the Case with Dwell Time
The problem of output regulation for hybrid systems hav-ing linear flow and jump maps is considered, under theassumption that the relevant time domain satisfies a dwelltime condition but is otherwise unknown. A characteri-zation of the steady-state motions achieving regulation isprovided in terms of hybrid generalizations both of the in-variant subspace algorithm and of the Francis equations.The two proposed approaches are compared, and relationswith the case without dwell time are highlighted.
Daniele CarnevaleUniversita di Roma ”Tor Vergata”[email protected]
Laura Menini, Mario Sassano, Sergio GaleaniUniversita di [email protected], [email protected],[email protected]
MS6
Stabilization of Switched Affine Systems by Meansof State Dependent Switching Laws
This presentations addresses the stabilization problem fora class of switched affine systems. Qualitative conditionsfor the existence of stabilizing switching laws dependent onthe systems state will be presented. The proposed method-ology is based on the use of an equivalent bilinear modelof the original switched system. Furthermore, constructiveconditions for local stabilization will presented by emulat-ing locally classical controllers. The proposed conditionscan be easily reformulated as numerically tractable linearmatrix inequalities.
Laurentiu Hetel
CT15 Abstracts 85
Ecole Centrale de [email protected]
Emmanuel BernuauIRCCyN UMR CNRS [email protected]
MS6
Geometric Methods for Switching Systems
This contribution reviews the basic aspects of the geomet-ric approach to control and regulation problems in linearswitching systems. It is shown that the geometric approachprovides tools and methods for characterizing, in a struc-tural sense, the solvability of non interacting control prob-lems, as well as of regulation problems, for different classesof switching systems. Both the cases in which the switchingsignal is measurable and that in which it is not measurableare considered.
Anna Maria PerdonUniversita Politecnica delle [email protected]
MS6
Stability Issues in Disturbance Decoupling forSwitching Linear Systems
Disturbance decoupling – i.e., the problem of making theoutput insensitive to undesired inputs – is a classical prob-lem of control theory and a main concern in control ap-plications. Hence, it has been solved for many classes ofdynamical systems, considering both structural and sta-bility requirements. As to decoupling in linear switchingsystems, several stability formulations apply. The aim ofthis contribution is pointing out different definitions of sta-bility and devising corresponding synthesis algorithms.
Elena ZattoniUniversity of [email protected]
MS7
Max-Plus Fundamental Solution Semigroups forOptimal Control Problems
Recent work concerning the development of fundamentalsolution semigroups for specific classes of optimal controland related problems is unified and generalized. By ex-ploiting max-plus linearity, semiconvexity, and semigroupproperties of the corresponding dynamic programming evo-lution operator, two types of max-plus fundamental solu-tion semigroup are presented. These semigroups, referredto as max-plus primal and max-plus dual space fundamen-tal solution semigroups (respectively), consist of horizonindexed max-plus linear max-plus integral operators. Theyfacilitate the propagation of value functions, and hence thesolution of Hamilton-Jacobi-Bellman equations, to longertime horizons via max-plus convolutions. Their applica-tion to specific classes of optimal control problem is alsosummarised.
Peter M. DowerThe University of [email protected]
William McEneaneyUniversity of California at San Diego
Huan ZhangThe University of [email protected]
MS7
On Average Control Generating Families for Sin-gularly Perturbed Optimal Control Problems
It is known that, under certain conditions, the dynamics ofthe slow components of a singularly perturbed (SP) con-trol system is approximated by solutions of the averagedsystem, in which the role of controls is played by measure-valued functions. A family of controls and the correspond-ing solutions of the fast subsystem is called average controlgenerating (ACG) if it generates a state-control trajectoryof the averaged system. We will state sufficient and neces-sary conditions of optimality of ACG families in problemsof optimal control considered on the solutions of the av-eraged system, and we will discuss a linear programmingbased approach to numerical construction of near optimalACG families. The theoretical results will be illustratedwith numerical examples.
Vladimir GaitsgoryDepartment of MathematicsMacquarie University [email protected]
MS7
High-Order Schemes for Stationary Hamilton-Jacobi-Bellman Equations
In this talk we consider stationary Hamilton-Jacobi-Bellman equations related to infinite horizon optimal con-trol problems or dynamic games. Our goal is to solve theseequations numerically using semi-Lagrangian schemes withhigh-order discretization in space. While for low order dis-cretizations monotonicity ensures convergence of the valueiteration, i.e., termination of the numerical computation,this is in general no longer the case for high-order meth-ods. Main contribution of the talk is to show how ε-monotonicity can be used in order to re-establish conver-gence and to present a selection of high-order schemes towhich this theory applies.
Olivier BokanowskiUniversite [email protected]
Maurizio FalconeUniversita di Roma “La Sapienza’, [email protected]
Roberto FerrettiDipartimento di Matematica e FisicaUniversita di Roma [email protected]
Lars GruneMathematical InstituteUniversitaet [email protected]
Dante KaliseRadon Institute for Computationaland Applied Mathematics (RICAM)
86 CT15 Abstracts
Hasnaa ZidaniENSTA ParisTech, INRIA [email protected]
MS7
Deterministic Control of Randomly-TerminatedProcesses
We will describe an efficient (noniterative) numericalmethod for a class of static HJB problems with freeboundary. Such equations arise in optimal controlof deterministic-up-to-termination finite-horizon processes,when the terminal time T is an exponentially distributedrandom variable. A part of this talk will be based on jointwork with J. Andrews.
Alexander VladimirskyDept. of MathematicsCornell [email protected]
MS8
Reconstruction of Independent Sub-Domains for aClass of Hamilton-Jacobi Equations and Applica-tion to Parallel Computing
A previous knowledge of the domains of dependence of aHamilton-Jacobi equation can be useful in its study andapproximation. Information of this nature is, in general,difficult to obtain directly from the data of the problem. Inthis talk we introduce formally the concept of independentsub-domain discussing its main properties and we providea constructive implicit representation formula. Using suchresults we propose an algorithm for the approximation ofthese sets that is shown to be relevant in the numericalresolution via parallel computing.
Adriano FestaRICAMAustrian Academy of [email protected]
MS8
Dynamic Programming for Path-Dependent Deter-ministic Control and Idempotent Expansion Meth-ods
It is often seen in control problems that the status of asystem is affected by not only a current state but also apast history of a trajectory. In this presentation, we willtalk about dynamic programming arguments for optimaldeterministic control under path-dependent dynamics andcosts. We show that the path-dependent continuous-timevalue function defined on an infinite-dimensional space canbe approximated by time-discretized path-dependent valuefunctions which, on the other hand, are given on finite-dimensional spaces. To compute the discrete-time path-dependent value function, we use idempotent expansionmethods. We will discuss particular cases where idempo-tent expansions work.
Hidehiro KaiseGraduate School of Engineering ScienceOsaka University
MS8
Staticization and Associated Hamilton-Jacobi andRiccati Equations
The use of stationary-action formulations for dynamicalsystems allows one to generate fundamental solutions forclasses of two-point boundary-value problems (TPBVPs).One solves for stationary points of the payoff as a func-tion of inputs, a task which is significantly different fromthat in optimal control problems. Both a dynamic pro-gramming principle (DPP) and a Hamilton-Jacobi partialdifferential equation (HJ PDE) are obtained for a class ofproblems subsuming the stationary-action formulation. Al-though convexity (or concavity) of the payoff may be lost asone propagates forward, stationary points continue to ex-ist, and one must be able to use the DPP and/or HJ PDEto solve forward to such time horizons. In linear/quadraticmodels, this leads to a requirement for propagation of so-lutions of differential Riccati equations past finite escapetimes.
William McEneaneyUniversity of California at San [email protected]
Peter M. DowerThe University of [email protected]
MS8
On the Use of Non-Stationary Policies for Station-ary Infinite-Horizon Markov Decision Processes
We consider infinite-horizon stationary γ-discountedMarkov Decision Processes, for which it is known thatthere exists a stationary optimal policy. Using Value andPolicy Iteration with some error ε at each iteration, it iswell-known that one can compute stationary policies thatare 2γ
(1−γ)2ε-optimal. After arguing that this guarantee is
tight, we develop variations of Value and Policy Iterationfor computing non-stationary policies that can be up to2γ1−γ
ε-optimal.
Boris Lesner, Bruno [email protected], [email protected]
MS9
Yield-Analysis of Different Coupling Schemes forInterconnected Bio-Reactors
Bio-chemical reaction networks are more and more adaptedto be used for the production of fine chemicals. Due tothe appearance of intermediate species which influence thesingle reaction steps, a single compartment approach forthe implementation of such a reaction may not be opti-mal. Multi-compartment approaches however might havethe potential to increase the yield of desired product if thecoupling of the compartments is chosen appropriately. Amodel based approach is presented to identify and analyzesuch coupling schemes for a specific enzyme cascade as anexample system.
Wolfgang HalterUniversity of [email protected]
CT15 Abstracts 87
Nico KressInstitute of Technical BiochemistryUniversitat [email protected]
Konrad Otte, Sabrina Reich, Bernhard HauerUniversity of [email protected],[email protected],[email protected]
Frank AllgowerUniversitat [email protected]
MS9
A Simulation-based Approach for Solving Optimi-sation Problems with Steady State Constraints
Ordinary differential equations (ODEs) are widely used tomodel biological, (bio-)chemical and technical processes.The parameters of these ODEs are often estimated fromexperimental data using ODE-constrained optimisation.This article proposes a simple simulation-based approachfor solving optimisation problems with steady state con-straints. This simulation-based optimisation method is tai-lored to the problem structure and exploits the local geom-etry of the steady state manifold and its stability proper-ties. A parameterisation of the steady state manifold isnot required. We prove local convergence of the methodfor locally strictly convex objective functions. Efficiencyand reliability of the proposed method are demonstratedin two examples.
Anna Fiedler, Fabian TheisHelmholtz Zentrum [email protected],[email protected]
Jan HasenauerHelmholtz Zentrum [email protected]
MS9
A Control Theory for Stochastic Biomolecular Reg-ulation
The tight regulation of the abundance of cellular con-stituents in the noisy environment of the cell is a criticalrequirement for several biotechnology and therapeutic ap-plications. Here we present elements of a new regulationtheory at the molecular level that accounts for the noisynature of biochemical reactions and provides tools for theanalysis and design of robust control circuits at the molec-ular level. Using these ideas, we propose a new regulationmotif that implements an integral feedback strategy thatrobustly regulates a wide class of reaction networks. Toolsfrom probability and control theory are then used to showthat the proposed control motif preserves the stability ofthe overall network, while steering the population of anyregulated species to a desired set point.
Mustafa KhammashControl Theory and Systems Biology D-BSSEETH-Zurich; 4058 Basel (CH)[email protected]
Ankit Gupta, Corentin Briat
ETH [email protected], [email protected]
MS10
Impulse Control of Non-Uniformly Ergodic Pro-cesses with Average Cost Criterion
We study a problem of impulse control of a Markov processthat maximises the average cost per unit time criterion:
lim infT→∞
1
TEx
{∫ T
0
f(Xs)ds−∞∑i=1
1τi≤T c(Xτi−, ξi)},
where f is a running reward and c ≥ 0 is an impulse cost.We characterise optimal strategies via a solution to an aux-iliary Bellman equation. The novelty of the paper is a gen-eral treatment of models in which (Xt) is supported onunbounded space and not uniformly ergodic. Our resultshave applications in balancing of energy systems and inmanaging inventories. Based on a joint work with �LukaszStettner.
Jan PalczewskiUniversity of [email protected]
MS10
Ergodic Stopping Problems
The lecture is devoted stopping problems of Markov pro-cesses with functional without discount rate. We show con-tinuity of the value function and existence of optimal stop-ping time. For this purpose we have to impose variousergodic conditions on Markov processes. In general we areinterested in the case when we don’t have uniform ergod-icity. We show the above results under different sets ofassumptions and consider also the case with general dis-count rate. The talk is based on a joint paper with J.Palczewski.
Lukasz W. StettnerInstitute of [email protected]
MS10
A Measure Approach for Continuous InventoryModels: Discounted Cost Criterion
This paper examines a single-item inventory process, mod-elled by a one-dimensional SDE, which incurs discountedcosts. The manager may increase the current inventorylevel but not reduce the inventory level. This paper pro-vides very minimal conditions which imply that an optimalordering policy exists in the class of (s, S) processes. Thestochastic problem is imbedded in two different linear pro-grams over a space of measures. The ultimate solutionrelies on duality theory in linear programming.
Kurt HelmesHumboldt University of [email protected]
Richard StockbridgeUniversity of Wisconsin - [email protected]
Chao ZhuUniversity of Wisconsin-Milwaukee
88 CT15 Abstracts
MS10
Representation Formulas for Solutions of IsaacsIntegro-PDE and Construction of Almost OptimalStrategies
We will present sub- and super-optimality inequalities ofdynamic programming for viscosity solutions of Isaacsintegro-PDE associated with two-player, zero-sum stochas-tic differential game driven by a Levy type noise. Thisimplies that the lower and upper value functions of thegame satisfy the dynamic programming principle and theyare the unique viscosity solutions of the lower and up-per Isaacs integro-PDE. Our method uses PDE techniquesand is based on regularization of viscosity sub- and super-solutions of Isaacs equations to smooth sub- and super-solutions of slightly slightly perturbed equations, and ap-proximate optimal synthesis. It is constructive and pro-vides a fairly explicit way to produce almost optimal con-trols and strategies.
Shigeaki KOikeTohoku [email protected]
Andrzej J. SwiechGeorgia TechDepartment of [email protected]
MS11
Viability Radius and Robustness for a class of Lin-ear Systems
We consider the problem of robust viability and viabilityradius for a class of linear disturbed systems. The problemconsists in the determination of the smallest disturbancef , for which a given viable state z0 do not remains viable.We also consider the problem of the determination of thesmallest disturbance f for which the viability set V iabfKis empty, which we call the Minimal Lethal Disturbance(MLD). This work is motivated by the problem of MinimalLethal Dose in toxicology.
Abdes Samed BernoussiFaculty of Sciences and Techniques, tangier, [email protected]
Mina Amharref, Mustapha OuardouzFST, [email protected], [email protected]
MS11
Constrained Optimal Control of Bilinear Systems:Application to An HVAC System
We investigate the constrained optimal control problemof bilinear systems. We minimize a quadratic cost func-tional over a set of admissible controls given by Uad ={u ∈ L2(0, T,Rm) : umin ≤ u ≤ umax and α ≤〈v, u〉L2(0,T,Rm) ≤ β}, using functional analysis tools. Wedevelop algorithms that allow to compute the optimal con-trol, and we apply our approach to an HVAC (HeatingVentilating and Air Conditioning) system, where the totalconsumed energy must not exceed a given ceiling.
Nihale El Boukhari
Faculty of Sciences [email protected]
El Hassan ZerrikUniversite Moulay Ismail - [email protected]
MS11
A Viability Analysis for Structured Model of Fish-ing Problem
In this work we study a structured fishing model, basi-cally displaying the two stages of the ages of a fish pop-ulation, which are in our case juvenile, and adults. Weassociate to this model two constraints: one of ecologicaltype ensuring a minimum stock level, the other one of eco-nomic type ensuring a minimum income for fishermen. Theanalytical study focuses on the compatibility between thestate constraints and the controlled dynamics. Using themathematical concept of viability kernel, we define a set ofconstraints combining the guarantee of consumption and astock of resources to be preserved at all times.
Mounir JerryUniversite Ibn Tofaı[email protected]
Chakib JerryEquipe EIMA, Departement de MathematiquesFaculty of [email protected]
MS11
A Viability Analysis of Fishery Controlled by In-vestment Rate
This work presents a stock/effort model describing bothharvested fish population and fishing effort dynamics. Thefishing effort dynamic is controlled by investment whichcorresponds to the revenue proportion generated by theactivity. The dynamics are subject to a set of economicand biological state constraints. The analytical study fo-cuses on the compatibility between state constraints andcontrolled dynamics. By using the mathematical conceptof viability kernel, we reveal situations and managementoptions that guarantee a sustainable system.
Nadia RaissiFaculty of Sciences [email protected]
C SanogoIbn Tofail University, Faculty of [email protected]
Slimane BenmiledUniversite de Tunis-El Manar Institut Pasteur de [email protected]
MS12
Dynamic Programming Using Radial Basis Func-tions
We propose a discretization of the time-discrete Hamilton-Jacobi-Bellman equation in optimal control in space by ra-dial basis functions in combination with a moving leastsquares projection type operator (aka ’Shepards method’).
CT15 Abstracts 89
We show convergence of the associated fixed point itera-tion, demonstrate the simplicity of the implementation bya corresponding Matlab code and present several numericalexperiments from optimal control.
Oliver JungeCenter for MathematicsTechnische Universitaet Muenchen, [email protected]
Alex SchreiberCenter for MathematicsTechnische Universitat [email protected]
MS12
A Spectral Assignment Approach for the GraphIsomorphism Problem
In this presentation, we will propose a heuristic for thegraph isomorphism problem that is based on the eigen-decomposition of the adjacency matrices. If the graphspossess repeated eigenvalues, which typically correspondto graph symmetries, finding isomorphisms is challenging.By repeatedly perturbing the adjacency matrices, it is pos-sible to break symmetries of the graphs without changingthe isomorphism. This heuristic approach can be used toconstruct a permutation which transforms GA into GB .
Stefan KlusFreie Universitat [email protected]
Tuhin SahaiUnited [email protected]
MS12
Graphical Model Based Representation of Dynam-ical Systems
Bayesian Networks are widely used to characterize thejoint dependence between random variables in multivari-ate problems due to their compactness and availability ofefficient learning/ inference algorithms. This talk high-lights the incorporation of deterministic relations, whichmay either be learned or explicitly embedded, within theframework of Bayesian networks to improve model fidelitywhile reducing complexity. Further, we motivate the needof this work by presenting concrete practical examples fromengineering domain.
Kushal Mukherjee, Blanca Florentino LianoUnited Technologies Research Center - [email protected], [email protected]
Ashutosh TewariExxonMobil Research & Engineering CompanyAnnandale, New [email protected]
Anarta GhoshUnited Technologies Research Center - [email protected]
MS12
From Geometry to Topology in Mobile Robotics:
Localization and Planning
In this talk, I will provide an overview of some recent workon localization and planning for mobile agents in a un-known/partially known environment using qualitative in-formation abstracted from dense metric data. By modelingthe problem from a topological perspective and using re-cent advances in the area of algebraic topology, we willderive methods for localization as well as planning strate-gies.
Alberto SperanzonUnited Technologies Research [email protected]
MS13
Discrete-time Control for Systems of InteractingObjects with Unknown Random Disturbance Dis-tributions: A Mean Field Approach
We are concerned with stochastic control systems com-posed of a large number N of interacting objects sharinga common environment. The dynamic of each object isdetermined by a stochastic difference equation, where therandom disturbance density is unknown to the controller.The system is modeled as a Markov control process and isanalyzed according to the mean field theory. Then, com-bining the mean field limit with a suitable statistical esti-mation method of the density, we construct control policieswhich are nearly asymptotically optimal for the N-system,under a discounted optimality criterion.
J. Adolfo Minjarez-Sosa, Carmen Higuera-ChanDepartamento de Matematicas, Universidad de [email protected], carg [email protected]
Hector [email protected]
MS13
Stationary Almost Markov Perfect Equilibria inDiscounted Stochastic Games
We study discounted stochastic games with Borel stateand compact action spaces depending on the state vari-able. The transition probability is a convex combinationof finitely many probability measures depending on statesand it is dominated by some finite measure on the statespace. Our main result establishes the existence of sub-game perfect equilibria, which are stationary (the equilib-rium strategy is determined by a single function of thecurrent and previous states of the game).
Andrzej NowakUniversity of Zielona [email protected]
Anna JaskiewiczInstitute of Mathematics and Computer ScienceWroclaw University of [email protected]
MS13
On Risk Processes Controlled by Investment andReinsurance
This contribution investigates insurance models for which
90 CT15 Abstracts
the risk/reserve process can be controlled by reinsuranceand investment in the financial market. Assuming thatthe company can control its wealth process over time intwo different ways: the reinsurance level and the amountof capital invested in the risky asset, the main objectivesof these works are to search the probability that the com-pany eventually becomes insolvent. A recent innovativeapproach uses continuous time Semi-Markov processes tounify the time of events that produce changes in the riskprocess, say claim arrivals and price changes of the riskyasset. Additional capital injection elements may be consid-ered by the company in order to maintain its wealth overa desired level. The finite horizon problem is faced andpartial solutions are presented.
Rosario RomeraStatistics Dept, Univ. Carlos III de [email protected]
MS13
On the Vanishing Discount Factor Approach forMarkov Decision Processes with Weakly Continu-ous Transition Probabilities
This note deals with average cost Markov decision pro-cesses with Borel state and control spaces, possibly un-bounded costs and non-compact action subsets, and weakcontinuous transition law. Based on recent results ofFeinberg, Kasyanov and Zadoianchuk (MOR 37, 591-607,2012), this note provides an elementary proof of the exis-tence of average cost optimal stationary policies using thevanishing discount factor approach.
Oscar Vega-AmayaDepartamento de MatematicasUniversidad de Sonora, [email protected]
MS14
Non-degenerate Forms of the Extended Euler-Lagrange Condition for State Constrained OptimalControl Problems
We consider state constrained optimal control problems inwhich the dynamic is represented in terms of a differen-tial inclusion, and the state and the end-point constraintsare closed sets. We shall discuss simple examples which il-lustrate how the interplay among the state constraint, theleft-end point constraint and the velocity set might influ-ence the possibility to apply the necessary conditions foroptimality in the non-degenerate form. We show that thisis actually a common feature for general state constrainedoptimal control problems.
Piernicola Bettiol, Nathalie KhalilUniversite de Bretagne OccidentaleBrest, [email protected], [email protected]
MS14
Analytical Study of Optimal Control InterventionStrategies for Ebola Epidemic Model
Abstract not available.
Ellina V. GrigorievaTexas Woman’s UniversityDepartment of mathematics and computer sciences
MS14
Budget-Constrained Infinite Horizon Optimal Con-trol Problem
In this talk a class of infinite horizon optimal control prob-lems with an isoperimetric constraint, also interpreted asa budget constraint, is considered. The problem settingincludes a weighted Sobolev space as the state space. Weinvestigate the question of existence of an optimal solutionand establish a Pontryagins Type Maximum Principle asa necessary optimality condition including a transversal-ity condition. Which influence the isoperimetric constraintmay have on the feasible set and on the existence of anoptimal solution is illustrated in details on examples.
Valeriya Lykina, Sabine PickenhainBrandenburg University of Technology Cottbus, [email protected], [email protected]
MS14
Optimal Control of Epidemiological Seir Modelswith L1-Objectives and Control-State Constraints
Optimal control is an important tool to determine vacci-nation policies for infectious diseases. For diseases trans-mitted horizontally, SEIR compartment models have beenused. Most of the literature on SEIR models deals withcost functions that are quadratic with respect to the con-trol variable, the rate of vaccination. In this paper, we con-sider L1-type objectives that are linear with respect to thecontrol variable. Various pure control, mixed control–stateand pure state constraints are imposed. For all constraints,we discuss the necessary optimality conditions of the Max-imum Principle and determine optimal control strategiesthat satisfy the necessary optimality conditions with highaccuracy. Since the control variable appears linearly inthe Hamiltonian, the optimal control is a concatenationof bang-bang arcs, singular arcs and boundary arcs. Forpure bang-bang controls, we are able to check second-ordersufficient conditions.
Maria d Rosario de PinhoFaculdade de Engenharia da Universidade do [email protected]
Helmut MaurerUniversitat MunsterInstitut fur Numerische und Angewandte [email protected]
MS15
Robust Mean-Field Games to Model Emulation inOpinion Dynamics
Abstract not available.
Dario BausoDept of Chemical EngineeringUniversity of Padova
CT15 Abstracts 91
MS15
Monotonicity Methods for Mean-Field Games
Abstract not available.
Diogo GomesKing Abdullah Univeristy of Science and [email protected]
MS15
Continuous Time Mean Field Consumption-Accumulation Modeling
We consider continuous time mean field consumption-accumulation games. The capital stock evolution of eachagent is based on the Cobb-Douglas production functionand takes into account stochastic depreciation. The indi-vidual HARA-type utility depends on both the own con-sumption and relative consumption. We analyze the fixedpoint problem of the mean field game. The individualstrategy is obtained as a linear feedback with the gain re-flecting the collective behaviour of the population.
Minyi HuangCarleton UniversitySchool of Mathematics and [email protected]
Son L. NguyenCarleton [email protected]
MS15
The Evolutionary Game of Pressure and Resistance
We extend the framework of evolutionary inspection game(put forward recently by the authors and his co-workers)to a large class of conflict interactions between a majorplayer and a large group of small players. The results areapplied to the analysis of the processes of inspection, cor-ruption, cyber-security, counter-terrorism, epidemiology,interaction of humans with their environment and manyother. The contribution will develop the ideas expressedin the author’s preprint ’The evolutionary game of pres-sure (or interference), resistance and collaboration’ (2014),http://arxiv.org/abs/1412.1269
Vassili KolokoltsovStatistics Dept, University of [email protected]
MS16
Numerics and Optimal Control for Phase-FieldModels of Multiphase Flow
Flow of mixtures of incompressible fluids with complexfluid interactions (surface tensions, contact angles) can bedescribed by a system of (multicomponent) Cahn-Hilliard-Navier-Stokes equations. We propose finite element basednumerical approximations of non-smooth phase-field mod-els for mixtures of incompressible fluids with variable den-sities and viscosities. We discuss theoretical and practicalissues related to the proposed numerical approximations.We also discuss numerical approaches for optimal control
of the models.
Lubomir BanasDepartment of Mathematics, Bielefeld [email protected]
MS16
Model Predictive Control of Two-Phase Flow Us-ing a Diffuse-Interface Approach
We present a nonlinear model predictive control frameworkfor closed-loop control of two-phase flows. The fluid is mod-eled by a thermodynamically consistent diffuse interfacemodel proposed in [H. Abels, H. Garcke, G. Grun, Thermo-dynamically consistent, frame indifferent diffuse interfacemodels for incompressible two-phase flows with differentdensities, M3AN, 22(3), 2012] and allows for fluids of dif-ferent densities and viscosities. We adapt the concept of in-stantaneous control to construct finite dimensional closed-loop control strategies for two-phase flows. We providenumerical investigations which indicate that finite dimen-sional instantaneous control is well suited to stabilize two-phase flows.
Michael HinzeUniversitat HamburgDepartment [email protected]
Christian KahleUniversity of [email protected]
MS16
Drag Optimisation in a Stationary Navier-StokesFlow Using a Phase Field Approach
We present a phase field formulation for boundary ob-jective functionals in shape optimisation with stationaryNavier-Stokes flow. With an additional Ginburg-Landauregularisation, we prove existence of a minimiser and de-rive first order necessary optimality conditions for a generalfunctional. The same results can be deduced for the dragfunctional, and via a formal asymptotic analysis, we showthat the sharp interface description of the drag optimisa-tion problem can be recovered from the phase field model.
Kei-Fong LamUniversitat Regensburg, Fakultat fur [email protected]
MS16
Optimal Control of a Semidiscrete Cahn-Hilliard/Navier-Stokes System with VariableDensities
In this talk we consider a time discretization of the Cahn-Hilliard/Navier-Stokes system with variable densities byAbels-Garcke-Grun and study an associated optimal con-trol problem. It focus is on the non-smooth double-obstaclepotential and distributed control action. Existence of min-imizers are shown and first-order optimality conditions arederived by a Yosida type approximation. The resulting sta-tionarity system corresponds to a function space version ofC-stationarity.
Michael HintermullerDepartment of Mathematics, Humboldt-University ofBerlin
92 CT15 Abstracts
Tobias Keil, Donat WegnerHumboldt University of [email protected], [email protected]
MS17
Feedback Control of Vortex Shedding Using Inter-polatory Model Reduction
We demonstrate the linear feedback control of vortex shed-ding in flows with one or two circular cylinders whererotation is used as the actuation mechanism. Reduced-order models of the linearized system are computed us-ing interpolatory model reduction and the computed feed-back control laws are shown to be effective in stabiliz-ing both steady-state and time-averaged flows for low-Reynolds number flows. The feedback control designs arealso used to determine the effective placement of sensors.
Jeff Borggaard, Serkan GugercinVirginia TechDepartment of [email protected], [email protected]
MS17
Model Reduction Based Feedback Control of theMonodomain Equations
Optimal control of reaction-diffusion systems arising inelectric cardiophysiology has become an important researchtopic. The monodomain equations represent a reasonablyaccurate model for the electric potential of the humanheart. In view of terminating cardiac arrhythmia, feed-back methodologies are of particular interest. In this talk,it is shown that the PDE-ODE structure of the linearizedmonodomain equations leads to a system that is not nullcontrollable but that can still be stabilized by finite dimen-sional controllers. This allows for constructing the con-troller based on model reduction techniques. While thereduced model is obtained from the linearized system, itis shown that it locally stabilizes the nonlinear system aswell.
Tobias BreitenUniversity of [email protected]
Karl KunischKarl-Franzens University GrazInstitute of Mathematics and Scientific [email protected]
MS17
Balanced POD Model Reduction for ParabolicPDE Systems with Unbounded Input and OutputOperators
Balanced POD is a data-based model reduction algorithmthat has been widely used for linearized fluid flows andother linear parabolic PDE systems with inputs and out-puts. We consider balanced POD algorithms for such sys-tems when the input and output operators are unbounded,as can occur when control actuators and sensors are locatedon the boundary of the physical domain. We discuss com-putational challenges, standard and modified algorithms,
and convergence theory.
Weiwei HuUniversity of Southern [email protected]
John SinglerMissouri S&TMathematics and [email protected]
MS17
Reduced-Order Surrogate Models for Closed-LoopControl
A stabilizing feedback control is computed for a semilin-ear parabolic PDE utilizing a nonlinear model predictive(NMPC) method. In each level of the NMPC algorithmthe finite time horizon open loop problem is solved by areduced-order strategy based on proper orthogonal decom-position. A stability analysis is derived for the combinedalgorithm so that the lengths of the finite time horizonsare chosen in order to ensure the asymptotic stability ofthe computed feedback controls.
Stefan VolkweinUniversitat KonstanzDepartment of Mathematics and [email protected]
Alessandro AllaDepartment of MathematicsUniversity of Hamburg, [email protected]
Maurizio FalconeUniversita di Roma “La Sapienza’, [email protected]
MS18
Gamkrelidze-Like Maximum Principle for OptimalControl Problems with State Constraints
This report addresses necessary conditions of optimalityfor optimal control problem with state constraints in theform of the Pontryagin’s Maximum Principle (MP). Forsuch problems, these conditions were first obtained by R.V.Gamkrelidze in 1959 and subsequently published in theclassic monograph by the four authors. His MP was ob-tained under a certain regularity assumption on the opti-mal trajectory. Somewhat later, in 1963, A.Ya. Dubovit-skii and A.A. Milyutin proved another MP for problemswith state constraints. In contrast with the MP of R.V.Gamkrelidze, this MP was obtained without a priori reg-ularity assumptions, and, thereby, it degenerates in manycases of interest. Later, under an additional assumption ofcontrollability of the optimal trajectory, other versions ofthe MP have been obtained so that they no longer degen-erate. Here, we suggest a MP in a form close to the oneproposed by R.V. Gamkrelidze but without any a prioriregularity assumptions on the optimal trajectory. However,the absence of regularity assumptions does not ensure thenondegeneracy of this MP. Therefore, we prove that, undercertain additional conditions of controllability relatively tothe state constraints at the end-points, or regularity of thereference control process, degeneracy will not occur, sincean appropriate non-triviality condition will be satisfied.
Aram Arutyunov
CT15 Abstracts 93
Moscow State [email protected]
Dmitry KaramzinComputing Centre of the Russian Academy of Sciencesdmitry [email protected]
Fernando L. PereiraPorto [email protected]
MS18
Pontryagin Principle in Infinite-DimensionalDiscrete-Times Problems
We present Pontryagin principle in infinite-dimensionalinfinite-horizon discrete-times optimal control for systemswhich are governed by difference equations or by differenceinequations. We use techniques of optimization in Banachordered spaces.
Mohammed BachirUniversite Paris [email protected]
MS18
The Euler Lagrange Equation and the Regularityof Solutions to Variational Problems
In this talk we will consider the problem of minimizing
∫Ω
[L(∇v(x)) + g(x, v(x))]dx
with boundary conditions v ∈ u0 +W 1,1(Ω) and, assuminga solution u to exist, we will focus on the problem of the va-lidity of the Euler-Lagrange equation for the solution andon the main application of this equation, namely to provethe regularity of the solution itself. We will present anoverview of the state of the art with respect to the valid-ity of the Euler-Lagrange equation, as well as some recentresults and some open problems. We shall then considerthe problem of the regularity of the solution: we mini-mize an integral functional over a space of functions hav-ing first order weak derivatives and, under some reasonableconditions, it turns out the the solution has second orderderivatives. We shall try to clarify the mechanism of thisphenomenon and present some recent results in this direc-tion.
Arrigo CellinaUniversita degli Studi di [email protected]
MS18
Subdifferentials of Nonconvex Integral Functionalsin Banach Spaces: A Gelfand Integral Representa-tion
We investigate subdifferential calculus for integral func-tionals on nonseparable Banach spaces. To this end, wepresent a new approach in which the Clarke and Mor-dukhovich subdifferentials of an integral functional are re-graded as a Gelfand integral of the subdifferential mappingof an integrand. Main results are applied to stochastic DPwith discrete time, and the differentiability of the value
function is demonstrated without any convexity assump-tion.
Nobusumi SagaraDepartment of EconomicsHosei [email protected]
Boris MordukhovichDepartment of Mathematics,Wayne State [email protected]
MS19
A Cubature Based Algorithm to Solve DecoupledMcKean-Vlasov Forward-Backward SDEs
As shown by Carmona, Delarue and Lachapelle (2012),the solution of a Mean-Field Game problem (and also theone of the related optimization of McKean-Vlasov type dy-namics problem) is linked to a system of forwardbackwardstochastic differential equations with coefficients depend-ing on the marginal distributions of the solutions. Wecall those types of equations McKean Vlasov Forward-Backward SDEs (MKV-FBSDE). In this talk, I will in-troduce an algorithm to solve decoupled MKV-FBSDEs,which appear in some stochastic control problems in amean field environment. We will start by defining a de-terministic algorithm to approximate weakly a MKV- For-ward SDE, as an alternative to the usual approximationmethods based on interacting particles. The algorithmis based on the cubature method of Lyons and Victoir(2004), and given enough regularity of the coefficients ofthe equation, it can be parametrized to obtain any givenorder of convergence. Then, we show how to construct im-plementable algorithms to solve decoupled MKV-FBSDEs.We give two algorithms and show that they have conver-gence of order one and two under appropriate regularityconditions. Finally, we proceed to illustrate our results bymeans of some numerical examples. This is a joint workwith P.E. Chaudru de Raynal
Camilo A. Garcia TrillosUniversity College London,[email protected]
MS19
”Phase Diagram” of a Simple Mean Field Game
We present a detailed analysis about a simple mean fieldgame model called “the seminar problem’ after [O. Gueant,J.-M. Lasry and P.-L. Lions, 2010]. This model is charac-terized by the fact that every agent optimizes his trajectorywith respect to a simple random event (the seminar start-ing time) which derives from the collective behavior. Inthe mean field limit, this event becomes deterministic anda rather thorough understanding of the solutions can beachieved. In particular, for a sensible class of initial con-ditions, distinct behaviors can be associated to differentdomains of the parameter space.
Thierry GobronUniversite de Cergy-Pontoise, [email protected]
Denis UllmoLaboratoire de physique theorique et modeles statistiquesCNRS Universite Paris-Sud,Orsay, France
94 CT15 Abstracts
Igor SwiecickiLPTM, Universite de Cergy Pontoise &[email protected]
MS19
Mean Field Games Equilibrium in a SIR Vaccina-tion Model
Recent debates concerning the innocuity of vaccines withrespect to the risk of the epidemic itself lead to vaccinationcampaign failures. We analyze, in a SIR model, whetherindividuals driven by self interest can reach an equilibriumwith the society. We show, in a Mean Field Games context,that an equilibrium exists and discuss the price of anarchy.Finally, we apply the theory to the 2009-2010 Influenza A(H1N1) vaccination campaign in France.
Laetitia LaguzetUniversite [email protected]
MS19
Fokker-Planck Optimal Control Problems
The Fokker-Planck (FP) equations are partial differentialequations describing the time evolution of the probabil-ity density function (PDF) of stochastic processes. Theseequations are of parabolic type corresponding to the PDFof Ito processes, and of hyperbolic type for the PDFof piecewise deterministic processes. For FP equationson bounded domains, we investigate the Chang-Cooperscheme for space discretization and first- and second-orderbackward time differencing. We prove that the resultingspace-time discretization schemes are accurate, condition-ally stable, conservative, and positivity-preserving. Forthe case of unbounded domains, the Hermite spectral dis-cretization method is applied and analyzed as well. Next,two optimal control formulations based on the FP equa-tions are discussed in order to control the correspondingPDFs. To approximate the solutions, the Hermite spectraldiscretization method is applied. Within the framework ofHermite discretization, we obtain sparse-band systems ofordinary differential equations. We analyze the accuracy ofthe discretization schemes by showing spectral convergencein approximating the state, the adjoint, and the controlvariables that appear in the FP optimality systems.
Masoumeh MohammadiInstitut fur Mathematik,Universitat [email protected]
MS19
On the Solvability of Risk-Sensitive Linear-Quadratic Mean-Field-Type Teams and Games
In this paper, we formulate and solve mean-field-type teamand game problems described by a linear stochastic dynam-ics of McKean-Vlasov type and a quadratic or exponential-quadratic cost functional for each player. The optimalstrategies of the players are given explicitly using a sim-ple and direct method based on square completion and aGirsanov-type change of measure. This approach does notuse the well-known solution methods such as the StochasticMaximum Principle and the Dynamic Programming Prin-ciple. Sufficient conditions for existence and uniqueness of
best response strategy to the mean of the state and themean-field equilibrium, are provided.
Hamidou TembineLSS, CNRS-Supelec-Univ. Paris Sud, [email protected]
Boualem [email protected]
MS20
Long and Winding Central Paths
We disprove a continuous analog of the Hirsch conjectureproposed by Deza, Terlaky and Zinchenko, by construct-ing a family of linear programs with 3r + 4 inequalities indimension 2r+ 2 where the central path has a total curva-ture in Ω(2r/r). Our method is to tropicalize the centralpath in linear programming. The tropical central path isthe piecewise-linear limit of the central paths of parameter-ized families of linear programs viewed through logarithmicglasses.
Xavier AllamigeonCMAP, Ecole [email protected]
Pascal BenchimolEDF R&D, Departement [email protected]
Stephane GaubertINRIA and CMAP, Ecole [email protected]
Michael JoswigTechnische Universitat [email protected]
MS20
A Max-Plus Fundamental Solution Semigroup fora Class of Lossless Wave Equations
A new max-plus fundamental solution semigroup is pre-sented for a class of lossless wave equations. This newsemigroup is developed via formulation of the action prin-ciple as an optimal control problem for the wave equationsof interest, followed by the construction of a max-plus fun-damental solution semigroup for this optimal control prob-lem using dynamic programming. An application of thissemigroup to solving two-point boundary value problemsis discussed via an example.
Peter M. DowerThe University of [email protected]
William McEneaneyUniversity of California at San [email protected]
MS20
Tropicalizing Semialgebraic Pivoting Rules, OrHow to Solve Mean Payoff Games in PolynomialTime on Average
We introduce an algorithm which solves mean payoff games
CT15 Abstracts 95
in polynomial time on average, assuming the distributionof the games satisfies a flip invariance property on the setof actions associated with every state. The algorithm is atropical analogue of the shadow-vertex simplex algorithm,which solves mean payoff games via linear feasibility prob-lems over the tropical semiring. The proof relies on theobservation that certain semi-algebraic pivoting rules canbe tropicalized.
Xavier AllamigeonCMAP, Ecole [email protected]
Pascal BenchimolEDF R&D, Departement [email protected]
Stephane GaubertINRIA and CMAP, Ecole [email protected]
MS20
On the Regulation Problem for Tropical LinearEvent Invariant Dynamical Systems
Tropical linear event-invariant systems describe the firingdynamics for timed event graphs with fixed times. In thiscontext, the regulation problem can be defined as the prob-lem of controlling the inputs so a given specification, de-scribed by a semimodule, is achieved. It will be shown that,under some technical assumptions, this regulation problemcan be reduced to a two-sided eigenproblem, which in turncan be solved using parametric mean payoff games.
Vinicius GoncalvesUnveristy Federal Minas [email protected]
Laurent HardouinISTIA / LISA - Angers [email protected]
Carlos Andrey MaiaUniversity Federal Minas Gerais, Belo Horizonte [email protected]
MS21
Modeling and Estimation in Control of ImmuneResponse to BK Virus Infection and Donor Kid-ney in Renal Transplant Recipients
In this presentation we discuss the feedback control prob-lem that results from the involuntary immune-suppressionthat is a standard therapy for organ transplant patients.We develop and validate with bootstrapping techniquesa mechanistic mathematical model of immune responseto both BK virus infection and a donor kidney based onknown and hypothesized mechanisms in the literature. Themodel presented does not capture all the details of the im-mune response but possesses key features that describe avery complex immunological process. We then estimatemodel parameters using a least squares approach with atypical set of available clinical data. Sensitivity analysiscombined with asymptotic theory is used to determine thenumber of parameters that can be reliably estimated giventhe limited number of observations.
H. Thomas BanksNorth Carolina State Univ
Dept of Math & Ctr for Rsch [email protected]
MS21
Sensitivity Analysis and Control in the LaminaCribrosa
We discuss sensitivity analysis with respect to importantbiological parameters (Lame coefficients, intra-ocular pres-sure and retrolaminar tissue pressure) for a poroelasticmodel describing the lamina cribrosa in the eye. It is be-lieved that the biomechanics of the lamina cribrosa playsan important role in the retinal ganglion cell loss in glau-coma. Our goal is to reveal which parameters are mostinfluential and need to be controlled in order to preventthe development of glaucoma.
Lorena BociuN. C. State UniversityRaleigh, [email protected]
MS21
Approximation Methods for Feedback Stabilizationof Boussinesq Equations
Pure Dirichlet boundary control of thermal fluids systemsleads to technical issues of control compatibility for 3Dproblems. In this paper we replace the pure Dirichletproblem with an approximating Robin boundary conditionwhich eliminates the compatibility condition. We showthe resulting Neumann/Robin boundary control problemis well posed and can be used to locally exponential stabi-lize the Boussinesq equations. Numerical results are givento illustrate the method and convergence of the approxi-mation scheme.
John A. BurnsVirginia TechInterdisciplinary Center for Applied [email protected]
MS21
Control of the Cardiovascular-Respiratory Systemunder External Perturbations
Exploiting the fact that in the combined cardiovascular-respiratory system the partial pressure of CO2 in arterialblood is regulated to 40 mm Hg we present results on thereaction of the system to external perturbations using theEuler-Lagrange formulation of the corresponding optimalcontrol problem. Numerical issues concerning stiffness ofthe resulting two-point boundary value problem will bediscussed.
Doris H. FuertingerRenal Research Institute New [email protected]
Franz KappelDepartment of Mathematics and Scientific ComputingUniversity of [email protected]
MS22
Lookback Option Pricing for Regime-Switching
96 CT15 Abstracts
Jump Diffusion Models
We will introduce a numerical method to price the Euro-pean lookback floating strike put options where the un-derlying asset price is modeled by a generalized regime-switching jump diffusion process. In the Markov regime-switching model, the option value is a solution of a coupledsystem of nonlinear integro-differential partial differentialequations. Due to the complexity of regime-switchingmodel, the jump process involved, and the nonlinearity,closed-form solutions are virtually impossible to obtain.We use Markov chain approximation techniques to con-struct a discrete-time Markov chain to approximate the op-tion value. Convergence of the approximation algorithmsis proved. Examples are presented to demonstrate the ap-plicability of the numerical methods.
Zhuo JinUniversity of Melbourne, [email protected]
Linyi QianEast China Normal [email protected]
MS22
Approximation of Basket CDS Price on DefaultSensitive Regime Switching Model
In this work, we derive the sufficient conditions for the con-vergence of the approximation of the basket CDS price viathe weak convergence method. Particularly, the volatilityof the underlying risk neutral price switches among finitemany regimes driven by the default events occurred in thepast.
Qingshuo SongCity University of Hong KongDepartment of [email protected]
MS22
A Multi-Scale Approach to Limit Cycles with Ran-dom Perturbations Involving Fast Switching andSmall Diffusion
This talk is devoted to multi-scale stochastic systems. Themotivation is to treat limit cycles under random perturba-tions involving fast random switching and small diffusion,which are represented by the use of two small parameters.Associated with the underlying systems, there are averagedor limit systems. Suppose that for each pair of the param-eters, the solution of the corresponding equation has aninvariant probability measure με,δ, and that the averagedequation has a limit cycle in which there is an averaged oc-cupation measure μ0 for the averaged equation. Our maineffort is to prove that με,δ converges weakly to μ0 as ε→ 0and δ → 0 under suitable conditions. We also examine ap-plication to a stochastic predator-prey model. Moreover,some numerical examples will also be reported.
H.N. DangWayne State [email protected]
N.H. DuHanoi National [email protected]
George YinWayne State UniversityDepartment of [email protected]
MS22
An Optimal Mean-Reversion Trading Rule undera Markov Chain Model
This paper is concerned with a mean-reversion tradingrule.In contrast to most market models treated in the liter-ature, the underlying market is solely determined by a two-state Markov chain. The major advantage of such Markovchain model is its striking simplicity and yet its capabilityof capturing various market movements. The purpose ofthis paper is to study an optimal trading rule under such amodel. The objective of the problem under consideration isto find a sequence stopping (buying and selling) times so asto maximize an expected return. Under some suitable con-ditions, explicit solutions to the associated HJB equations(variational inequalities) are obtained. The optimal stop-ping times are given in terms of a set of threshold levels. Averification theorem is provided to justify their optimality.Finally, a numerical example is provided to illustrate theresults.
Qing ZhangUniversity of GeorgiaDepartment of [email protected]
MS23
Lmi Formulation of Analysis and Control ProblemsInvolving Fractional Order Models
The aim of the talk is to present several methods based onLinear Matrix Inequalities (LMI) to analyze properties andto design control laws for systems modeled by fractionaldifferential equations. First, model is written as a pseudostate space representation whose limitations are reminded.Then, LMI formulations for stability analysis, stabilizationand H∞ control are proposed. Finally, some perspectivesare drawn in order to overcome the limitations induced bypseudo state space representation.
Christophe Farges
University of Bordeaux, IMS Laboratory (CRONE Team),CNRS UMR [email protected]
Jocelyn SabatierUniversity of Bordeaux, IMS Laboratory (CRONE Team)CNRS UMR [email protected]
MS23
Diffusive Representations for the Stability Analysisand Numerical Simulation of Fractional PDEs
Fractional integrals and derivatives can be equivalentlytransformed into Diffusive representations, allowing forwell-posedness and stability analysis of fractional ODEsor PDEs, seen as coupled systems. Though a Lyapunovfunctional can be proposed explicitely, a lack of pre-compactness of the trajectories is to be found, we resortto Arendt-Batty theorem to conclude on asymptotic sta-bility. Moreover, on a linear fractional wave equation withnon-constant coefficients, a more general Integral repre-
CT15 Abstracts 97
sentation is used to analyze and numerically simulate thesystem in low dimension.
Thomas HelieCNRS UMR 9912Ircam Centre Georges [email protected]
Denis MatignonISAE-Supaero, University of [email protected]
Christophe PrieurCNRS [email protected]
MS23
Stabilizability Properties of Fractional Delay Sys-tems of Neutral Type
We consider the stabilizability of fractional delay systemsof neutral type including the delicate case of systems whichpossess a chain of poles clustering the imaginary axis. Frac-tional rational controllers are investigated first and areshown to be very efficient for proper systems but not be welladapted for strictly proper systems with some parameteruncertainties. Second, the stabilizability by some classesof fractional controllers with delays is examined. Finally,some illustrative examples are given.
Le Ha Vy Nguyen, Catherine [email protected], [email protected]
MS23
On the Two Degree-of-Freedom Control of Frac-tional Systems
We propose a methodology to design a two-degree-of-freedom fractional control system. First, the feedback con-troller is obtained, for a class of fractional systems, by solv-ing a weighted H∞ model-matching problem to achievesome robustness specifications. Then, an optimal para-metric feedforward signal is synthesized by input-outputinversion of the fractional system dynamics. Finally, theweighting function and the feedforward signal parametersare optimized through a combined min-max problem.
Fabrizio PadulaDipartimento di Ingegneria dell’InformazioneUniversita degli Studi di [email protected]
Antonio VisioliUniversity of BresciaDepartment of Mechanical and Industrial [email protected]
MS24
Sensing and Control in Symmetric Networks
We examine the relation between the symmetry structureof linear finite-dimensional systems and their controllabil-ity, where symmetry property indicates that the state tran-sition matrix A commutes with a finite non-trivial groupof matrices. We show that representation theory of finitegroups constitutes a framework that allows generalizationof some existing results on controllability of interconnected
distributed systems. Computational aspects of optimal ac-tuator placement are addressed. Main ideas are illustratedwith several telling examples.
Miroslav BaricUnited Technologies Research CenterEast [email protected]
Michael DellnitzUniversity of [email protected]
Stefan KlusFreie Universitat [email protected]
MS24
Observation and Control of Ensembles of LinearSystems
Parameter dependent linear systems define natural classesof ensembles, i.e., infinite networks of systems. We applymethods from complex approximation theory to character-ize controllability and observability for ensembles of linearsystems, where the controls or observations are indepen-dent of the system parameters. By sampling at finitelymany parameters, this leads to new tools for robust con-trol and estimation of large scale networks.
Uwe R. HelmkeUniversitat WuerzburgDepartment of [email protected]
Schoenlein MichaelInstitute of Mathematics, University of Wuerzburg,[email protected]
MS24
Dynamic Intrinsic Variables for Data Fusion andState Reconstruction
In this talk, we show how data-driven Koopman spec-tral analysis can be applied to the problem of data fusionand/or nonlinear state estimation. Our approach uses Ex-tended Dynamic Mode Decomposition to approximate theleading Koopman eigenfunctions, which we use as a setof intrinsic coordinates that embed different sets of mea-surements in a common space. We apply our method tothe FitzHugh-Nagumo PDE, and map point-wise measure-ments to principal component coefficients.
I. G. KevrekidisPrinceton [email protected]
Matthew O. WilliamsProgram in Applied and Computational MathematicsPrinceton [email protected]
MS24
A Chaotic Dynamical System That Paints andSamples
In this work, we develop a novel algorithm to reproduce
98 CT15 Abstracts
paintings and photographs. Combining ideas from ergodictheory and control theory, we construct a chaotic dynam-ical system with predetermined statistical properties. Be-yond reproducing paintings this approach is expected tohave a wide variety of applications such as uncertaintyquantification and sampling for efficient inference in ma-chine learning. We then explore the use of this algorithmfor assigning limited resources to nodes in a graph.
Tuhin SahaiUnited [email protected]
George A. MathewUniversity of California, Santa [email protected]
Amit SuranaSystem Dynamics and OptimizationUnited Tecnologies Research Center (UTRC)[email protected]
MS25
Bang-Bang Type Nash Equilibrium Points forNonzero-Sum Stochastic Differential Games
It is by now well known that non-zerosum differentialgames are connected to multi-dimensional BSDEs with,usually, non Lipschitz generators. In the case when thepayoffs of the players of the game depend only on the ter-minal value of the controlled system, the generator of theassociated BSDE could even be discontinuous. Howeverwe show that a Nash equilibrium point for this specificgame exists in the Markovian framework. This Nash equi-librium point is of bang-bang type. This is a joint work byS.Hamadne and Rui MU.
Said Hamadene, Rui MuUniversity of Le [email protected], [email protected]
MS25
Credit Default Swaps with Bessel Bridges
In this work we propose the valuation of credit defaultswap using the so-called Bessel bridges to model the creditndex process. The intuition behind this assumption is thatBessel bridges, by contruction, remain stricly positive untila fixed time T at which they hit zero for the first time.
Gerardo Hernandez-del-ValleBanco de [email protected]
MS25
Evolutionary Inspection Games
In this talk, we present a few developments of inspectiongames with an evolutionary perspective and the propertiesof their equilibria.
Wei YangUniversity of [email protected]
Vassili KolokoltsovStatistics Dept, University of [email protected]
Stamatios KatsikasUniversity of [email protected]
MS25
Study of Certain Stochastic Predator-Prey Models
Stochastic Predator-Prey models arise from many appli-cations in ecological and biological applications. Recentlysuch systems have drawn resurgent attentions. In this talk,we present some new perspective of study on such sys-tems. We treat permanence and ergodicity for both non-degenerate and degenerate cases. One new feature of ourresult is the characterization of the support of a uniqueinvariant probability measure. Convergence in total vari-ation norm of transition probability to the invariant mea-sure is also established. Related Kolmogorov systems withregime switching will also be investigated.
H.N. DangWayne State [email protected]
N.H. DuHanoi National [email protected]
George YinWayne State UniversityDepartment of [email protected]
MS26
Numerical Approaches for Bilevel Optimal ControlProblems with Scheduling Tasks
Abstract not available.
Matthias GerdtsUniversitaet der Bundeswehr [email protected]
MS26
An Example of Solving Hjb Equations Using SparseGrids
In this presentation, we show an example of solving the 6-DHJB equation for the optimal attitude control of a satelliteequipped with momentum wheels. To mitigate the curse-of-dimensionality, a computational method on sparse gridsis developed. The method is causality free, which enjoysthe advantage of perfect parallelism. The problem is solvedusing several hundred CPUs in parallel. The accuracy ofthe numerical solution is verified at a set of randomly se-lected sample points.
Wei KangNaval Postgraduate SchoolDepartment of Applied [email protected]
Lucas WilcoxDepartment of Applied MathematicsNaval Postgraduate School
CT15 Abstracts 99
MS26
Optimal Control of a Hyperbolic Conservation LawModeling Highly Re-Entrant Manufacturing Sys-tems
Highly re-entrant manufacturing systems common in semi-conductor manufacturing may be modeled by hyperbolicconservation laws with non-local velocity. We investi-gate the problem for L1 and positive measure-valued data,whereas previous results [Coron, Kawski, and Wang (2010)MR 2679644] and [Colombo, Herty, and Mercier (2011) MR2801323] established existence and uniqueness of solutionsfor the minimum-time optimal control problem and for L2
data.
Matthias KawskiDept. of Mathematics and StatisticsArizona State [email protected]
MS26
The Role of the Objective in Optimal ControlProblems Arising in Biomedical Applications
Mathematical models for biomedical problems generallyare described by nonlinear systems, often affine in the con-trols that represent, for example, drug concentrations inmodels for cancer chemotherapy or vaccination and treat-ment rates in epidemiological problems. It is natural toconsider these problems as optimization problems, for ex-ample, to minimize the tumor volume achievable with agiven amount of chemotherapeutic agents. As much as bi-ology offers insights into the dynamics of the underlyingsystem, there generally is little guidance about the choiceof the objective and this allows for considerable freedom.However, this choice strongly influences the structure of op-timal solutions seen. For example, controls are continuousif quadratic, L2-type functionals are minimized, but gen-erally have discontinuities if L1-type functionals are con-sidered. Necessary conditions for optimality based on thePontryagin maximum principle allow the computations ofextremals, but even in the L2 case do not guarantee evenlocal optimality of a numerically computed solution. Thussufficient conditions for optimality need to be verified andthese need to be customized to the problem under consid-eration. In this talk, we discuss the implications that thechoice of the objective has on the mathematical proceduresthat need to be employed (e.g., differences in the associ-ated flows of extremals) as well as relate the structure ofsolutions back to the biological background of the originalproblem.
Heinz SchaettlerWashington [email protected]
Urszula LedzewiczSouthern Illinois University, [email protected]
MS27
On the Interpretation of the Master Equation
Since its introduction by P.L.Lions in his lectures andseminars at the College de France, the Master equationhas attracted a lot of interest, and various points of view
have been expressed. There are several ways to introducethis type of equation. It involves an argument that isa probability measure, and Lions has proposed to workwith the Hilbert space of square integrable random vari-ables. So writing this equation is an issue. Its origin isanother issue. In this talk we discuss these various as-pects, and for the modeling we heavily rely on a seminarby P.L.Lions at the College de France on November 14,2014; see http://www.college-de-france.fr
Alain BensoussanThe University of Texas at Dallas andCity University of Hong Kong, Hong [email protected]
MS27
On Nonlinear Filtering Theory for McKean-VlasovSDEs
Partially observed stochastic dynamical systems whosestate equations are of McKean-Vlasov (MV) SDE type(and hence contain a measure term) are considered. Non-linear filtering equations are provided based on the classifi-cation that the measure term is stochastic or deterministic,and that either the state or the joint state and measureterm is estimated. The filtering equations in both normal-ized and unnormalized forms and, for some cases, equationsfor conditional densities are obtained.
Nevroz SenDept of Electrical and Computer EngMcGill [email protected]
Peter E. CainesMcGill [email protected]
MS27
From Kinetic to Macroscopic Models Through Lo-cal Nash Equlibria
We propose a mean field kinetic model for systems of ra-tional agents interacting in a game theoretical framework.This model is inspired from non-cooperative anonymousgames with a continuum of players and Mean-Field Games.The large time behavior of the system is given by a macro-scopic closure with a Nash equilibrium serving as the localthermodynamic equilibrium. Applications of the presentedtheory to social and economical models will be given.
Pierre DegondImperial College of London, Applied mathematics [email protected]
MS27
Nonlinear Filtering Problems in Partially ObservedMFG Control Theory
In Mean Field Games (MFG) with a major and many mi-nor agents the best response policies of the minor agentsdepend on the major agents state and the stochastic meanfield. The situation where the minor agents partially ob-serve the major agent’s state is considered and nonlinearfiltering equations for the major agent’s state when its dy-namics depend upon the mean field are obtained. The re-sults are then applied to the corresponding MFG problem.
100 CT15 Abstracts
Nevroz SenDept of Electrical and Computer EngMcGill [email protected]
Peter E. CainesMcGill [email protected]
MS28
On Pod and Krylov Methods for Solution of Alge-braic Riccati Equations
We propose a projection based method to solve large-scalealgebraic Riccati equations based on proper orthogonal de-composition. The method can take advantage of existingsimulation codes for linear systems, is easy to implementand produces very accurate solutions. We highlight con-nections to Krylov subspace methods and present a numer-ical example, where the matrices come from a high fidelitydiscretization of a two dimensional PDE.
Boris KramerVirginia [email protected]
John SinglerMissouri S&TMathematics and [email protected]
MS28
On Adi Approximate Balanced Truncation
Balanced truncation is a model reduction method forinput-output-systems governed by ordinary differentialequations which relies on the determination of the observ-ability and controllability Gramian matrices and providesan error bound in the H∞ norm. A variety of efficient nu-merical methods have been developed for balanced trunca-tion. In particular, the ADI iteration for determining theGramians has become very popular since it allows to de-termine reduced order models of large-scale systems. SinceADI iteration provides approximative solutions, it is natu-ral to wonder the effect of this approximation in the overallmodel reduction process. This is subject the talk, wherewe aim to present a backward error analysis: We first showthat ADI approximate balanced truncation in theory con-sists of exact balanced truncation of a certain artificial sys-tem, which is obtained from the original system via an L2-orthogonal projection of the impulse response. Numericalconsequences will be presented.
Timo ReisTechnische Universitat [email protected]
MS28
Trust Region POD for Optimal Control of a Semi-linear Heat Equation
An optimal control problem governed by a semilinear heatequation is solved using globalized inexact Newton meth-ods. The Newton step is computed by a conjugate gradi-ent algorithm. To reduce the computational effort a modelorder reduction approach based on proper orthogonal de-
composition (POD) is applied. By utilizing POD in a trustregion framework we can guarantee that the reduced-orderapproximation of the gradient is sufficiently accurate. Nu-merical results are presented and discussed.
Sabrina RoggUniversity of KonstanzDepartment of Mathematics and [email protected]
Stefan TrenzUniversitat KonstanzDepartment of Mathematics and [email protected]
MS28
Rb-Based Optimization with Parameter Functions
We solve parabolic partial differential equations using aspace-time variational formulation. We do not only allowparameters in the coefficients (for e.g. model calibration)but choose the initial condition as a parameter (function)as well. A reduced basis method is introduced that han-dles the parameter function and the corresponding infinitedimensional parameter space in a two-step Greedy proce-dure. In option pricing, this offers the possibility to usethe same reduced basis for different types of options asthey differ only by their initial value (assuming the samemodel approach). This is joint work with Antonia Mayer-hofer (Univ. of Ulm).
Antonia MayerhoferUniversity of [email protected]
Karsten UrbanInstitute of Numerical Mathematics, University of [email protected]
MS29
Acyclic Gambling Games
A gambling game is a two player zero stochastic game,played in discrete time, where each player controls a gam-bling house. A gambling house Γi of player i is a measur-able function that assigns to each xi ∈ Xi a nonempty setΓi(xi) of probability measures defined on the Borel sub-sets of Xi, where Xi is a metric compact set. Think totwo players in a Casino where xi is the fortune of playeri and Γi(xi) is the set of gambles available to player iwhen his fortune is xi. The gambling game is played asfollows. At stage t = 1, ..., knowing the past history ofstates (x1
1, x21, ..., x
1t , x
2t ), each player i chooses simultane-
ously as his opponent a probability σit ∈ Γi(xi
t). The newstates xi
t+1, i = 1, 2, are selected according to σit. The pair
(x1t+1, x
2t+1) is publicly announced and the game moves to
stage t+1. For each discount factor λ ∈]0, 1[, one can asso-ciate a game with total payoff
∑∞t=1 λ(1 − λ)t−1u(x1
t , x2t ),
where u is some continuous utility function. A standardapproach proves that this discounted game has a value vλ,which is the unique fixed point of a λ-Shapley operator.We prove that, if the gambling houses are non-expensiveand irreversible, the asymptotic value limλ→0 vλ exists andmay be characterized as the unique fixed point of a pair offunctional equations which extends the Mertens-Zamir sys-tem and the “Reduite’ operator.
Rida Laraki
CT15 Abstracts 101
CNRS and LAMSADE, Paris-Dauphine [email protected]
Jerome RenaultGremaq, Universite de [email protected]
MS29
Denjoy-Wolff Theorems for Hilbert’s and Thomp-son’s Metric Spaces
We shall discuss some recent results concerning the dynam-ics of fixed point free mappings on the interior of a normal,closed cone in a Banach space that are nonexpansive withrespect to Hilbert’s metric or Thompson’s metric. Amongother results, we show several Denjoy-Wolff type theoremsthat confirm conjectures by Karlsson and Nussbaum for animportant class of nonexpansive mappings. We shall alsosee how one can extend, and put into a broader perspec-tive, results by Gaubert and Vigeral concerning the linearescape rate of such nonexpansive mappings.
Bas LemmensSMSAS, University of [email protected]
Brian LinsHampden-Sydney [email protected]
Roger NussbaumMathematics DepartmentRutgers [email protected]
Marten WortelNorth-west University, Potchefstroom, South [email protected]
MS29
The Operator Approach to Zero Sum Games; Ap-plications to Games with short stage Duration
The operator approach to zero-sum repeated games con-sists in the study of the properties of the Shapley operatorsdescribing the recursive structure of the game, in order toinfer asymptotic properties on its values. After recallingimportant results in the field, we will consider in partic-ular the games with short stage duration defined by Ney-man (Dynamic Games and Applications, 2013) and estab-lish some of their asymptotic properties using the theoryof nonexpansive operators in Banach spaces.
Sylvain SorinUniversity Paris [email protected]
Guillaume VigeralUniversite Paris-Dauphine, [email protected]
MS29
Existence of Pure Optimal Uniform Strategies inPartially Observable Markov Decision Processe
We consider Partially Observable Markov Decision Pro-cesses. We prove that for any ε > 0, there exists a pure
strategy which is ε-optimal in any n-stage POMDP, pro-vided that n is big enough. Moreover, under this strategy,the expectation of the liminf of the random mean of thestage rewards is close to the optimal reward.
Bruno ZiliottoTSE Univ Toulouse [email protected]
Xavier VenelParis 1 [email protected]
MS30
Conjugate Times and Regularity of the MinimumTime Function with Differential Inclusions
We study the regularity of the minimum time function, T ,for a system with a general target, taking the state equationin the form of a differential inclusion. We first derive asensitivity relation which guarantees the propagation of theproximal subdifferential of T along any optimal trajectory.Then, we obtain the local C2 regularity of the minimumtime function along optimal trajectories by using such arelation to exclude the presence of conjugate times.
Piermarco CannarsaUniversity of Rome ”Tor Vergata”, [email protected]
MS30
Second Order Sensitivity Relations for the MayerProblem in Optimal Control
We investigate the value function, V, of a Mayer optimalcontrol problem. The second order sensituivity relationsare derived using solutions of the corresponding Riccatiequation, the co-state of the maximum principle and sec-ond order sub/superjets of V along optimal trajectories.By applying sensitivity analysis to exclude the presenceof conjugate points, we deduce that the value function istwice differentiable along any optimal trajectory startingat a point at which V is proximally subdifferentiable.
Piermarco CannarsaUniversity of Rome ”Tor Vergata”, [email protected]
Helene FrankowskaCNRS and IMJ-PRG UPMC Paris [email protected]
Teresa ScarinciUPMC (Paris) and U. Roma Tor [email protected]
MS30
Linear-Quadratic Optimal Control Probems withInfinite Horizon - Maximum Principle, Duality andSensitivity
We consider a class of infinite horizon optimal control prob-lems in Lagrange form involving the Lebesgue integral witha weight function in the objective. This special class ofproblems arises in the theory of economic growth, in pro-cesses where the time T is an exponentially distributedrandom variable and in problem of asymptotic feedbackstabilization of a linear control system. The problem is for-
102 CT15 Abstracts
mulated as optimization problem in Hilbert Spaces. Theseconsiderations give us the possibility to extend the admis-sible set and simultaneously to be sure that the adjointvariable belongs to a Hilbert space. For the class of prob-lems proposed, we can proof an existence result as well asPontryagin type Maximum Principle including transver-sality conditions. The convex duality theory developed forthis problem class provides sensitivity results.
Sabine PickenhainBrandenburg University of Technology Cottbus, [email protected]
MS30
Necessary Conditions for Optimal Control Prob-lems with Time Delays
We report on necessary conditions for free-time opti-mal control problems with time delay, recently derivedby Boccia and Vinter. The conditions cover problemswith general, non-smooth data and incorporate a newtransversality-type condition associated with the free end-time. They are accompanied by sensitivity relations, whichdescribe the effect of small parameter changes on the opti-mal cost. It is shown how the free-time conditions can beused to compute optimal controls.
Richard B. VinterImperial College, Exhibition Road, London SW7 2AZ, [email protected]
MS31
Demand Response-Enabled Optimal Control ofHVAC Systems in Buildings
Optimized control of HVAC system can potentially reducesignificant amount of energy consumption of buildings. Inthis work, we describe a model predicted control (MPC)framework that optimally computes the control profiles ofthe HVAC system considering the dynamic demand re-sponse signal, on-site storage of electricity, on-site gener-ation of electricity, greenhouse gas emission as well as oc-cupants comfort. The approach would determine how topower the HVAC system from the optimal combination ofgrid electricity, on-site stored electricity and on-site gener-ated electricity.
Raya HoreshIBM T.J. Watson Research [email protected]
Young M. LeeIBM T.J. Watson Reseach [email protected]
Leo LibertiIBM ”T.J. Watson” Research Center, Yorktown Heights,USALIX, Ecole Polytechnique, Palaiseau, [email protected]
Young Tae ChaeHyundai Engineering & Construction Co., LtdResearch and Development Division , Seoul, Republic [email protected]
Rui ZhangIBM T.J. Watson Reseach Center
MS31
Energy Use Forecast and Model Predictive Controlof Building Complexes
In this talk, we present a framework for forecasting and op-timization of energy dynamics of building complexes. Thisframework integrates a physics-based model with a time-series model to forecast and optimally manage building en-ergy. Physical characterization of the building is partiallycaptured by a collection of energy balance equations es-timated by a least squares technique and data generatedfrom the EnergyPlus model. The model is then used in anMPC framework to control set points.
Mohsen JafariIndustrial and Systems EngineeringRutgers, The State University of New [email protected]
Seyed VaghefiRutgers UniversityIndustrial and Systems [email protected]
MS31
A Binary Bilevel Algorithm: Application for RealTime Control of a Medium Voltage Electrical Net-work
Reporting from the SO-grid project: we present a new al-gorithm to solve binary bilevel programs. At each stepof the algorithm, we solve a binary linear slave program,check the feasibility for the master problem, and add a cutif the solution is not feasible. As an application, we showhow this algorithm can be used to solve a binary bilevelmodel for real time control of medium voltage electricalnetwork.
Pierre-Louis PoirionLIX-Ecole [email protected]
Sonia Toubaline, Leo LibertiEcole [email protected],[email protected]
Claudia D’AmbrosioCNRS, LIX, [email protected]
MS31
Real Time Control of Medium Voltage ElectricalDistribution Networks
Several electrical measurement devices are designed, devel-oped and deployed within the SO-grid project in order tomonitor and control a medium voltage electrical network inreal time. We present a mathematical model to determinethe minimum number and location of these devices to beplaced in the network and that ensure the convergence ofthe state estimation function. We also discuss some solu-tion methods and preliminary computational results.
Sonia ToubalineEcole Polytechnique
CT15 Abstracts 103
Pierre-Louis PoirionEcole [email protected]
Leo LibertiEcole [email protected]
Claudia D’AmbrosioCNRS, LIX, [email protected]
MS32
Optimal Distributed Control for Continuum PowerSystems
Large electrical power networks can be viewed as contin-uum systems which follow the dynamics of a second or-der nonlinear wave equation with constant voltage assump-tions. In this talk we generalize to time and space variantvoltages. Two optimal control problems are solved. Thefirst problem is when the mechanical power is the controlinput, while the second problem is when the variant voltagemagnitude is the control input under a generalized variantvoltage PDE constraint. Numerical results are presentedto illustrate the performance of the resulting closed loopcontrol systems for large power networks.
Samir SahyounUniversity of [email protected]
Seddik DjouadiDepartment of Electrical Engineering and ComputerScienceUniversity of Tenneessee, [email protected]
K. TomsovicUniversity of [email protected]
Suzanne M. LenhartUniversity of TennesseeDepartment of [email protected]
MS32
Decentralized Charging and Discharging Control ofPlug-in Electric Vehicles for Peak Load Shifting
Plug-in electric vehicles (PEVs) are energy storage devicesand distributed energy resources. Using advanced meter-ing infrastructure and communication technologies, we cancontrol PEVs for peak load shifting. In this paper, byallowing bidirectional power flow between PEVs and thegrid, we study the load flattening problem by regulatingPEVs’ charging and discharging process. A decentralizedalgorithm using iterative water-filling is developed. Theadvantages of our algorithm include reduction in compu-tational burden and privacy preserving.
Hao XingZhejiang UniversityHangzhao, [email protected]
Yuting MouZhejiang [email protected]
Minyue FuUniversity of [email protected]
Zhiyun LinZhejiang [email protected]
MS32
Incorporating Smart-Grid Operating Strategiesinto Off-Grid Electrification Planning
The introduction of smart meters with wireless communi-cation and sophisticated technology for fine-grained mon-itoring and control has revolutionized the possibilities fordeploying highly resilient and economically sustainable mi-crogrids for off-grid electrification. Traditional planningtools lack the flexibility to explore implications of operatingstrategies that leverage these capabilities. A new method ispresented for incorporating low-level, user-selected powermanagement policies into comprehensive microgrid plan-ning analysis to support comparative evaluation of alter-native implementations for first-access energy systems.
Jesse Thornberg, Gabriela HugCarnegie Mellon [email protected], [email protected]
Taha Salim UstinCarnegie Mellon University in [email protected]
Anthony Rowe, Bruce KroghCarnegie Mellon [email protected], [email protected]
MS32
Randomized Policies for Demand Dispatch
The paper concerns automated demand response fromon/off loads. It is assumed that there is one-way communi-cation from the grid operator to each load. The loads are ei-ther on or off – their power consumption is not continuouslyvariable. Local control at each load is defined by a family ofMarkov transition matrices, denoted {Pζ : ζ ∈ }. At timet, if the load receives the signal ζt from the grid operator,then it changes state to the value x′ with probability de-fined by the transition matrix, Pζt(x, x′); the randomnessis local, and hence independent of all other loads. A mean-field limit is used to obtain an input-output model, wherethe output is the aggregate power consumption. The mainresult is to show how these transition laws can be designedso that the linearized mean field model is minimum phaseat any operating point. This is achieved through a vari-ety of Markov chain analytical tricks based on Poisson’sequation.
Sean Meyn, Yue ChenUniversity of Florida
104 CT15 Abstracts
[email protected], [email protected]
MS33
Moreau Sweeping Processes on Banach Spaces
The sweeping process or Moreau’s process in a Hilbertspace (introduced and studied by J.J. Moreau in J.D.E. in1977) is an interesting problem in both Analysis and Me-chanics. In this talk I will present my last recent results onthe existence of solutions for several extensions to Banachspaces of Moreau sweeping processes and its variants.
Messaoud BounkhelDepartment of MathematicsKing Saud University, Saudi [email protected]
MS33
Control of Moreau’s Sweeping Process: Some Re-sults and Open Problems
In this talk we discuss some recent results of the theoryof Moreau’s sweeping processes including necessary condi-tions for the dynamic case. As open problems we discussthe dynamic programming for the controlled sweeping pro-cess, which is currently being investigated and establishinga suitable version of Pontryagin Maximum principle.
Giovanni ColomboUniversity PadovaDipartimento di [email protected]
MS33
Differential and Difference Inclusions and the Fil-ippov Theorem
This is a joint work with R. Baier and F. Lempio. Wesurvey some results on the continuous and discrete Filip-pov theorem on approximate solutions of differential anddifference inclusions and applications.
Elza M. FarkhiTel Aviv UniversitySchool of Mathematical [email protected]
MS33
Optimality Conditions for Optimal Control Prob-lems with Interval-Valued Objective Functions
This work examines continuous time optimal control prob-lems with interval-valued objective functions. For this, weconsider three concepts of order relations in the intervalspace to obtain optimality conditions for these problemsand obtain Pontryagin maximum principle type of opti-mality conditions for optimal control problems using theconcept of generalized Hukuhara derivative (gH-derivative)for interval-valued functions. We also illustrate our methodwith numerical examples.
Geraldo N. SilvaUniversidade Estadual Paulista - UNESPDepartment of Applied [email protected]
Ulcilea LealUniversidade Federal do Mato Grosso do Sul
Weldon LodwickDepartment of Mathematical SciencesUniversity of Colorado [email protected]
MS33
Differential Inclusions and Applications
My talk will deal with differential inclusions. Such evolu-tion problems appear when the state-variable is submittedto some constraints and therefore has to stay in an admis-sible set. Especially we will be interested in the study ofsweeping processes and of second order differential inclu-sions involving proximal normal cones. We propose to de-tail some results about these different problems by pointingout the geometrical assumptions regarding the admissiblesets. Furthermore we will consider some applications incrowd motion modelling and in granular media.
Juliette VenelLab de Mathematiques et leurs Applications deValenciennesUniversite Lille-Nord de [email protected]
MS34
A Dynamic Domain Decomposition for a Class ofSecond Order Hamilton-Jacobi Equations
We present a new parallel algorithm for the numerical so-lution of a class of second order Hamilton-Jacobi equationscoming from stochastic optimal control problems. Thenew method is an extension of the patchy domain decom-position technique developed in the recent joint work ofthe author with E. Cristiani, M. Falcone, and A. Picarelli(2012). The original method is modified to solve quite gen-eral nonlinear problems with possibly degenerate and con-trol driven diffusion. In particular, we show that, undersuitable relations between the data and the discretizationparameters, a remarkable acceleration of the parallel com-putation can be obtained. This is a joint work MaurizioFalcone.
Simone CacaceDipartimento di MatematicaUniversita di [email protected]
MS34
Convergence of An Hp-Collocation Method for Op-timal Control
A convergence theory is introduced for approximations ofcontinuous-time optimal control problems using an hp-collocation method based on Radau quadrature. Under as-sumptions of coercivity and smoothness, an hp discretiza-tion of an unconstrained control problem has a local mini-mizer and corresponding Lagrange multiplier that convergein the sup-norm to a local minimizer and costate of thecontinuous-time optimal control problem. The accuracy isimproved either by increasing the degree of the polynomialwithin a mesh interval or by refining the mesh. The con-vergence theorem is presented along with a brief overviewof the proof. This is a joint work with Hongyan Hou and
CT15 Abstracts 105
Anil V. Rao.
William HagerUniversity of [email protected]
MS34
Optimal Control for Irrigation Scheduling based onthe AquaCrop Model
We present a methodology based on numerical optimal con-trol to determine optimal irrigation scheduling under re-stricting water quotas. The objective function, which isnonlinear and non-smooth, is the expected seasonal yieldcalculated using the dynamic crop model AquaCrop. Bygradually increasing the value of the water quota, the con-vex function describing yield as a function of irrigation wa-ter as obtained. Irrigated maize in the region of Lombardia,Italy, is presented as example.
Raphael [email protected]
MS34
Computation of An Explicit Error Estimate for Op-timal Control Problems of Odes
Error estimates for the local solution of an optimizationproblem typically depend on the fineness of the discretiza-tion and on the smallest eigenvalue of a certain quadraticform (related to second-order sufficient optimality condi-tions). In this talk, we will consider the case of optimalcontrol problems of ODEs, discretized in time. The com-putation of the smallest eigenvalue, a delicate task, will bebased on a ”Riccati”-based approach, that we will explainwith the help of Schur complements.
Laurent PfeifferUniversity of [email protected]
MS34
Lie Brackets and Hamilton-Jacobi Inequalities
In relation with a control-affine system with a non nega-tive Lagrangian, we embed the corresponding Hamilton-Jacobi-Bellman equation in a more general equation. Inparticular, the latter is built from Lie brackets of the vectorfields involved in the dynamics. The supersolutions of thisextended equation can be regarded as Liapunov-like func-tions (here called Minimum Restraint Functions), which,besides yielding global asymptotic controllability, providean upper estimate on the minimum value.
Franco RampazzoUniversita di PadovaDipartimento di [email protected]
MS35
Parametric Robust Control Design
We present a new technique for tuning arbitrary linearcontrol structures against multiple plant models subjectto parametric uncertainties and against a variety of per-formance requirements. Our method is an inner relax-ation. Worst-case parametric scenarios are computed and
exploited to design robust controllers against parametricuncertainties. Our approach relies on two different non-smooth optimization techniques which operate in controllerand parameter spaces, respectively. Applications reveal agood balance between flexibility and effectiveness.
Pierre [email protected]
MS35
Robust Interference Control for Networks withLink Uncertainty
In multi-cell communication networks, the end users suf-fer not only from intra-cell interference and noise, but alsointer-cell interference. It is very important to control theseinterferences by precoding the transmitted signals to im-prove the quality of the received signals and maximize thenetwork throughput. Signal precoding must use the linkstate information, which is obtained through training andthus subject of uncertainty. In this talk, we show that therobust interference control is a concave program, which canbe solved effectively by very low-complexity iterations.
Tuan HoangUniversity of Technology, Sidney, AustraliaFaculty of Engineering and Information [email protected]
MS35
Bilinear Constrained Programming for Robust PIDController Design
A new design method of extended PID controllers achiev-ing robust performance is developed. Both robust stabiliza-tion and performance conditions are losslessly expressed bybi-linear constraints in the proportional-double derivativegains (kp, kdd) and the derivative-integral gains (ki, kd).Therefore, the considered PID control design can be effi-ciently solved by alternating optimization between (kp, kdd)and (ki, kd), where each alternating iteration is an infi-nite linear or infinite convex program. Furthermore, themethod works equally efficiently whenever even higher or-der differential or derivative terms are needed to be in-cluded in PID control to improve its robust stabilizabilityand performance capability. Numerical examples are pro-vided to show the viability of the proposed development.
Shigeyuki HosoeRIKEN-TRI Collaboration Center for Human-InteractiveRobot RNagoya, [email protected]
MS35
Computing the Structured Distance to Instability
Analysis and control of systems with uncertain real param-eters has been high on the agenda since the 1980s. In thistalk we investigate the computation of quantities like thedistance to instability of a nominally stable system withuncertain parameters, or the worst-case H-infinity normof a system over a given range of uncertain parameters.Such criteria allow to assess the robustness of a system,but their computation is NP-hard. We therefore developheuristic approaches, which are fast and reliable in prac-tice, and which can a posteriori be certified when used in
106 CT15 Abstracts
tandem with suitable global methods.
Dominikus NollUniversite Paul SabatierInstitut de [email protected]
MS36
Parameter Estimation in a Stochastic SystemModel for PageRank
The PageRank algorithm is used by Google as a way ofhierarchically indexing web pages in order to ensure thatit provides relevant and reputable search results. In thispaper, we present a stochastic system reformulation of thePageRank problem and establish strong consistency of theleast squares estimator of an unknown parameter in thesystem. Furthermore, we show that the least squares es-timator remains strongly consistent within a distributedrandomized framework for PageRank computation.
Cody E. Clifton, Bozenna J. Pasik-DuncanUniversity of [email protected], [email protected]
MS36
Classification of Alzheimer’s Disease Using Unsu-pervised Diffusion Component Analysis
The goal of this study is to classify magnetic resonance(MR) images of brains of patients with Alzheimers Disease(AD) and those without AD. An algorithm based on diffu-sion maps constructs coordinates that generate geometricrepresentations using the MRI. Diffusion maps arise frommodeling of data by stochastic differential equations. Thismethod also accounts for variability in calibration for dif-ferent patients. This is joint work with Thomas Strohmerfrom UC Davis.
Dominique DuncanDepartment of Mathematics, University of California [email protected]
MS36
Empirical Characteristic Function Methods in Sys-tem Identification
The objective of this talk is to extend the empirical char-acteristic function method to identify finite dimensionallinear stochastic systems driven by an i.i.d. noise process,the characteristic function of which is known to belong to aparametric class of characteristic functions given in closedform. The proposed method is essentially as efficient asthe maximum likelihood method. Our results will be sup-ported by extensive numerical experiments.
Laszlo GerencserMTA SZTAKI, Hungarian Academy of Sciences,Budapest, [email protected]
Mate ManfayGoldman Sachs Asset Management International,London,Great [email protected]
Balazs GerencserUniversite catholique de [email protected]
MS36
A Classification Based Perspective to Optimal Pol-icy Design for a Markov Decision Process
Classical approximate dynamic programming techniquesgenerally become impracticable in high-dimensions. Policysearch copes with this issue by considering a parameter-ized policy space. Here, we focus on discrete actions andintroduce a parameterization inspired by nearest-neighborclassification, each particle representing a state space re-gion mapped into a certain action. Locations and actionsare tuned via policy gradient with parameter-based explo-ration. The task of selecting an appropriately sized set ofparticles is solved through an iterative scheme.
Giorgio Manganini, Matteo Pirotta, Luigi Piroddi,Marcello RestelliPolitecnico di Milano, [email protected], [email protected],[email protected], [email protected]
Maria PrandiniDipartimento di Elettronica e InformazionePolitecnico di [email protected]
MS36
Shadow Price for General Discrete Time Models
In the case of market with proportional transaction costs(bid and ask price) we are looking for an artificial mar-ket with price without transaction costs such that opti-mal strategies and value functions on both markets are thesame. In the talk we shall consider a number of problemsarising in discrete time setting which lead first to so calledweak shadow price, the price depending on current finan-cial position, with the use of which we construct shadowprice. The talk is based on o joint paper with T. Rogala.
Lukasz W. StettnerInstitute of [email protected]
MS37
Partially Observable Markov Decision Processeswith General State, Action and Observation Sets
We describe sufficient conditions for the existence of opti-mal policies, validity of optimality equations, and conver-gence of value iterations for discounted partially observableMarkov decision processes with Borel state, action, andobservation sets. These conditions are: (i) the one-stepcost function is bounded below and K-inf-compact, (ii) thetransition probability is weakly continuous, and (iii) theobservation probability is continuous in total variation.
Eugene A. FeinbergStony Brook [email protected]
Pavlo Kasyanov, Michael ZgurovskyNational Technical University of Ukraine
CT15 Abstracts 107
[email protected], [email protected]
MS37
Inverse Problems and Dynamic Potential Games
Dynamic potential games are, roughly speaking, nonco-operative dynamic games whose equilibria can be foundby solving certain optimal control problem. One way tocharacterize some classes of dynamic potential games isthrough inverse problems. In this talk we present someresults about inverse problems in optimal control and dy-namic potential games. In particular, we characterize aclass of dynamic potential games whose Nash equilibriaand Pareto solutions coincide.
David Gonzalez-SanchezEscuela Superior de Economia, [email protected]
MS37
Equilibrium Characteristics of Default in a Cur-rency Area
Hernandez-del-Valle and Martinez-Garcia (2015) find thatdefault is the optimal decision of a sovereign government ina currency area after prolonged real exchange rate overval-uation. Our objective is to determine if default is Paretooptimal and/or Nash equilibrium.
Adrian Hernandez-del-ValleEscuela Superior de Economia, [email protected]
Martinez-Garcia Claudia I.SEPI-ESE-Instituto Politecnico [email protected]
MS37
Approximation of Denumerable State Continuous-Time Markov Games: Discounted and AveragePayoff Criteria
We consider a two-person zero-sum continuous-timeMarkov game with denumerable state space, general actionspaces, and unbounded payoff and transition rates. Wedeal with noncooperative equilibria for the discounted andthe average payoff criteria. We are interested in approxi-mating numerically the value and the optimal strategies ofthe game. We construct finite state and actions truncatedgame models, that can be explicitly solved, which convergein a suitably defined sense to the original game model. Westudy the convergence rate for the value of the games andwe illustrate our results with an application to a populationsystem.
Tomas Prieto-RumeauStatistics Dept, [email protected]
Jose Marıa [email protected]
MS38
No-Fold Conditions for Broken Extremals
We consider an optimal control problem whose extremals
are given by the flows of two competing Hamiltonians,not necessarily equal to lifts of vector fields. We assumethat there are only normal switching points (Kupka, 1987).Conjugacy for the resulting broken extremals may occur ator between switching times; we formulate a sufficient con-dition for strong optimality in terms of jumps on the Jacobifields which is related to the no-fold condition of Noble andSchattler (2002). As an application, we consider L1 mini-mization of the control of affine multi-input systems whosecontrol is restricted to the Euclidean ball.
Jean-Baptiste CaillauMath. InstituteBourgogne Univ. & [email protected]
Zheng Chen, Yacine ChitourUniv. Paris Sud & [email protected], [email protected]
MS38
On Sufficient Conditions for a Class of ConstrainedProblems with Indefinite Quadratic Functional
In [M.M.A. Ferreira, A.F. Ribeiro and G.V. Smirnov, LocalMinima of Quadratic Functionals and Control of Hydro-Electric Power Stations, JOTA, july 2014] some new suffi-cient conditions for a local minimum of a possibly indefinitequadratic functional were developed. That work was mo-tivated by the existence of non-isolated local minimizersassociated to a certain class of optimal control problems.We will present some further analysis of such sufficient con-ditions as well as some other applications.
M. Margarida A. FerreiraUniversidade do PortoFac. Engenharia, [email protected]
G. V. SmirnovUniversidade do [email protected]
MS38
On Strong Local Optimality of Concatenations ofBang and Singular Arcs
Abstract not available.
Laura PoggioliniDipartimento di Matematica e InformaticaUniversita di Firenze, [email protected]
MS38
The Turnpike Property in Optimal Control
The turnpike property emerged in the 50’s, after the worksby the Nobel prize Samuelson in econometry. It stands forthe general behavior of an optimal trajectory solution ofan optimal control problem in large time. This trajectorytrends to behave as the concatenation of three pieces: thefirst and the last arc being rapid transition arcs, and themiddle one being in large time, almost stationary, close tothe optimal value of an associated static optimal controlproblem. In a recent work with Enrique Zuazua, we haveestablished the turnpike property in a very general frame-work in finite dimensional nonlinear optimal control. We
108 CT15 Abstracts
prove that not only the optimal trajectory is exponentiallyclose so some (optimal) stationary state, but also the con-trol and the adjoint vector coming from the Pontryaginmaximum principle. Our analysis shows an hyperbolicityphenomenon which is intrinsic to the symplectic feature ofthe extremal equations. We infer a very simple and effi-cient numerical method to compute optimal trajectories inthat framework, with an appropriate variant of the shoot-ing method.
Emmanuel TrelatUniversite Pierre et Marie CurieParis, [email protected]
MS39
A Physics Based Approach to Model Discrepancyand Model Form Uncertainty for Design and Con-trol of Distributed Parameter Systems
Abstract not available.
John A. BurnsVirginia TechInterdisciplinary Center for Applied [email protected]
MS39
Optimal Boundary Control and Estimation ofParabolic PDEs Using Sum-of-Squares (SOS) Poly-nomials
We use SOS to design stabilizing and optimal controllersfor scalar parabolic PDEs with spatially distributed coef-ficients. We use point actuation via Dirichlet, Neumann,Robin and mixed boundary conditions and point measure-ments of state. Our approach is based on solving LOIs us-ing a convex parameterization of Lyapunov functions viapositive matrices. Objectives include include both expo-nential stability and minimum L2 gain. Numerical ex-amples show the accuracy is competitive with alternativessuch as backstepping.
Aditya GahlawatIllinois Institute of TechnologyUniversite de [email protected]
Matthew PeetArizona State [email protected]
MS39
Low-complexity Modeling of Partially AvailableSecond-order Statistics via Matrix Completion
We study the problem of completing partially known statestatistics of large-scale linear systems. The dynamical in-teraction between state variables is known while the direc-tionality of input excitation is uncertain. In particular, weseek to explain the data with the least number of possibleinput disturbance channels. This can be formulated as arank minimization problem, and for its solution, we employa convex relaxation based on the nuclear norm.
Armin Zare, Yongxin ChenUniversity of [email protected], [email protected]
Mihailo R. JovanovicElectrical and Computer EngineeringUniversity of [email protected]
Tryphon T. GeorgiouUniversity of [email protected]
MS39
Boundary Estimation for Infinite Dimensional El-liptic Cauchy Problem Using Observers
We design and prove the convergence of an iterative ob-server for boundary estimation problem for an elliptic equa-tion, namely, Cauchy problem for Laplace equation. TheLaplace equation is formulated as a first order system inone of the space variables with state operator matrix. Theconvergence of proposed iterative observer is establishedusing semigroup theory and the concepts of observabilityfor infinite dimensional systems. Numerical simulations areprovided to signify efficiency of the algorithm.
Meriem Laleg, Mohammed Usman [email protected], [email protected]
MS40
Model Order Reduction Approaches for the Op-timal Design of Permanent Magnets in Electro-Magnetic Machines
In an electromagnetic machine with permanent magnetsthe excitation field is provided by a permanent magnet in-stead of a coil. The center of the generator, the rotor,contains the magnet. Our optimization goal consists infinding the minimum volume of the magnet which gives adesired electromotive force. This results in an optimiza-tion problem for a parametrized partial differential equa-tion (PDE). We propose a goal-oriented model order reduc-tion approach to provide a reduced order surrogate modelfor the parametrized PDE which then is utilized in the nu-merical optimization. Numerical tests will be provided inorder to show the effectiveness of the proposed method.
Alessandro AllaDepartment of MathematicsUniversity of Hamburg, [email protected]
Michael HinzeUniversitat HamburgDepartment [email protected]
Oliver LassTechnische Universitaet Darmstadt [email protected]
Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematik
CT15 Abstracts 109
MS40
Reduced Basis Method for Multiobjective Opti-mization
We present a reduced order technique for the numericalsolution of PDE-constrained multiobjective optimization,where several objective functions have to be simultaneouslyoptimized. The idea is to find a solution which does notpenalize the optimization of any objective function andwhich is a good compromise for all the individual ones.In general, does not exist a single optimal solution, butthere exists a (possibly infinite) number of Pareto opti-mal solutions. In the multiobjective optimization theory,the Pareto optimality allows to determine efficient optimalpoints for all the considered objective functions [C. Hiller-meier. Nonlinear multiobjective optimization. A gen-eralized homotopy approach. Birkhaeuser Verlag, Basel,2001]. We apply the reduced basis method in this con-text where the constraints are given by parametric linearand semilinear PDEs [A.T. Patera and G. Rozza. Re-duced basis approximation and a posteriori error estima-tion for parametrized partial differential equations Version1.0. Copyright MIT, http://augustine.mit.edu, 2007], inorder to propose a reduced-order techniques to handle thecomputational complexity and resolution times and to en-sure a suitable level of accuracy.
Laura IapichinoUniversity of KonstanzDepartment of Mathematics and [email protected]
Stefan Volkwein, Stefan TrenzUniversitat KonstanzDepartment of Mathematics and [email protected], [email protected]
MS40
Reduced Order Models for Nonlinear PDE-Constrained Optimization and Control Problems
We review reduced basis methods for the efficient solutionof parametric optimization and parametrized control prob-lems dealing with nonlinear PDEs, by considering both a“reduce-then-optimize’ and an “optimize-then-reduce’ ap-proach. A simultaneous reduction of state and controlspaces is performed when dealing with parametrized con-trol problems. Moreover, efficient a posteriori error boundsenable to certify the solution of the reduced optimizationproblem. We present some numerical test cases dealingwith the optimal control of fluid flows.
Andrea ManzoniEPFL, [email protected]
Federico NegriMATHICSE-CMCS, Ecole Polytechnique Federale [email protected]
Alfio QuarteroniEcole Pol. Fed. de Lausanne
MS40
Application of Error Estimates for Nonlinear PODReduced Order Models
We consider the use of reduced order models in the cal-ibration of certain models in mathematical finance whichlead to the identification of parameters of a highly non-linear PDE. While the ROM fits the original system quitesuccessfully, the nonlinear dependence is very strong anda frequent refitting of the ROM is necessary. We observedthis numerically and try to find a theoretical justificationfor this behavior.
Ekkehard W. SachsUniversity of [email protected]
MS41
Ergodicity Condition for Zero-Sum Games
For zero-sum repeated stochastic games, basic questionsare whether the mean payoff per time unit is independentof the initial state, and whether this property is robust toperturbations of rewards. In the case of finite action spaces,we show that the answer to both questions is positive if andonly if an ergodicity condition involving fixed points of therecession function of the Shapley operator or reachabilityin directed hypergraphs is satisfied.
Marianne AkianINRIA Saclay–Ile-de-France and CMAP, [email protected]
Stephane GaubertINRIA and CMAP, Ecole [email protected]
Antoine HochartINRIA and CMAP, Ecole [email protected]
MS41
Strategically Enhanced Preferential Attachement,Coalition Building and Evolutionary Growth
We prove rigorous results on the convergence of variousMarkov decision models of interacting small agents to adeterministic evolution on the distributions of the statespaces of small players, paying the main attention to situ-ations with an infinite state space of small players. Theseinclude the strategically enhanced extensions of the modelsof evolutionary growth, coalition building and preferentialattachment. Applications include processes of banks orfirms merging, as well as the processes of emerging coop-eration.
Vassili KolokoltsovStatistics Dept, University of [email protected]
MS41
Target Defense Differential Game with a Closed-
110 CT15 Abstracts
Form Solution
A pursuit-evasion game in the plane is considered where anattacker (A) strives to come as close as possible to a Tar-get set (T) before being intercepted by the Defender (D)whereas D tries to intercept A as far away from T as pos-sible; the players A and D have simple motion a la Isaacs.The game terminates when A reaches T without havingbeen intercepted by D, or A comes as close as possible tothe target set T, at which time he is captured by D. Wealso comment on the case where the target T is a dynamicpoint target and the D and T team play cooperatively todefeat A.
Meir PachterAir Force Inst of TechnologyDept of Electrical [email protected]
MS41
Development of An Idempotent Algorithm for aNetwork-Delay Game
A game is considered where the communication networkof the first player is explicitly modeled. The second playermay induce delays in this network, while the first playermay counteract such actions. Costs are modeled throughexpectations over idempotent probability measures. Idem-potent algebras are used to obtain an algorithm for solutionof the game.
Amit PandeyUniv. California, San [email protected]
William McEneaneyUniversity of California at San [email protected]
MS42
Coupling MPC and DP Methods for the NumericalSolution of Optimal Control Problems
We consider the approximation of an infinite horizon opti-mal control problem which combines a first step based onModel Predictive Control (MPC) in order to have a quickguess of the optimal trajectory and a second step where wesolve the Bellman equation in a neighborhood of the ref-erence trajectory. In this way we obtain a local version ofthe classical DP approach. We present the main featuresof these new technique and illustrate its effectiveness bysome numerical tests.
Maurizio FalconeUniversita di Roma “La Sapienza’, [email protected]
Alessandro AllaDepartment of MathematicsUniversity of Hamburg, [email protected]
Giulia FabriniUniversita di [email protected]
MS42
Recent Computational Techniques for Dynamic
Programming on Hybrid Systems
The notion of hybrid system has been recently introducedto give a unified framework for control systems mixing dis-crete and continuous control actions. In this talk, we re-view some recent researches on the approximation of Dy-namic Programming equations for hybrid systems, includ-ing convergence and error estimates for numerical schemes,acceleration techniques based on policy iteration, and con-struction of a quasi-optimal feedback. Moreover, we showsome numerical tests on real (although relatively simple)applications.
Roberto FerrettiDipartimento di Matematica e FisicaUniversita di Roma [email protected]
Achille SassiENSTA [email protected]
Hasnaa ZidaniENSTA ParisTech, INRIA [email protected]
MS42
Local Optimization Algorithms for the Approxima-tion of Hamilton-Jacobi-Bellman Equations
We introduce local optimization strategies for DynamicProgramming-based approximations of Hamilton-Jacobiequations. In particular, semi-Lagrangian schemes requirethe local minimization of the Hamiltonian with respectto the control variable. For this purpose, we set a semi-smooth Newton method and a first-order primal-dual al-gorithm, both leading to accurate optimal control fields.We present different examples assessing the performanceand accuracy of the proposed scheme.
Dante KaliseRadon Institute for Computationaland Applied Mathematics (RICAM)[email protected]
Axel KroenerINRIA Saclay and CMAP, Ecole [email protected]
Karl KunischKarl-Franzens University GrazInstitute of Mathematics and Scientific [email protected]
MS42
Speeding Up Model Predictive Control ViaAl’brekht’s Method and Its Extensions
The methods that we propose for speeding up MPC arebased on Albrekhts method for solving HJB equations. Al-brekht showed that the Taylor series around an operatingpoint of the optimal cost and optimal feedback of an infinitehorizon continuous time nonlinear optimal control problemcould found degree by degree. We extend this method todiscrete time nonlinear optimal control problems. The se-ries provide a terminal cost and terminal feedback for MPCthat is defined on a larger domain. This allows a shortertime horizon thereby speeding up MPC. We extend the se-ries approach to find the Taylor series of the optimal cost
CT15 Abstracts 111
and optimal feedback around a optimal trajectory. Thisspeeds up MPC by yielding a longer interval for the realtime computation.
Arthur J. KrenerNaval Postgraduate SchoolDepartment of Applied [email protected]
MS43
Second Order Analysis of State-ConstrainedControl-Affine Problems
In this talk we establish new second order necessary andsufficient optimality conditions for a class of control-affineproblems with a scalar control and a scalar state constraint.These optimality conditions extend to the constrained stateframework the Goh transform, which is the classical toolfor obtaining a generalization of the Legendre condition.We propose a shooting algorithm to solve numerically thisclass of problems and we provide a sufficient condition forits local convergence. We present examples to illustratethe theory.
Marıa Soledad [email protected]
Frederic BonnansInria-Saclay and CMAP, Ecole [email protected]
Bean-San GohCURTIN SARAWAK RESEARCH INSTITUTE,[email protected]
MS43
Second-Order Necessary Conditions in PontryaginForm for Optimal Control Problems
We say that optimality conditions for an optimal controlproblem are in Pontryagin form if they only involve La-grange multipliers for which Pontryagin’s minimum prin-ciple holds. This restriction to a subset of multipliers isa strengthening for necessary conditions, and enables suf-ficient conditions to give strong local minima [Milyutin,Osmolovskii]. We consider optimal control problems withpure state and mixed control-state constraints, and wepresent here first- and second-order necessary conditionsin Pontryagin form, relying on a technique of partial relax-ation [Dmitruk].
Frederic Bonnans, Xavier DupuisInria-Saclay and CMAP, Ecole [email protected], [email protected]
Laurent PfeifferUniversity of [email protected]
MS43
Second-Order Necessary Optimality Conditions forthe Mayer Problem Subject to a General ControlConstraint
We discuss second order necessary optimality conditionsfor the Mayer optimal control problem with an arbitrary
closed control set U ⊂ Rm. Using second order tangents,we show that if a control u(·) is optimal, then an associ-ated quadratic functional is nonnegative on elements in thesecond order jets to U along u(·). Our proofs are straight-forward and do not use embedding of the problem into aclass of infinite dimensional problems.
Helene FrankowskaCNRS and IMJ-PRG UPMC Paris [email protected]
Nikolai P. OsmolovskiiSystems Research Institute, Polish Academy of Sciencesul. Newelska 6, 01-447, Warszawa, [email protected]
MS43
A Second-Order Maximum Principle for State-Constrained Control Problems
In this talk we present second-order necessary optimalityconditions for control problems in the presence of purestate constraints, obtained using second-order tangents tothe set of trajectories. Through a second-order variationaldifferential inclusion we obtain a point-wise second-ordermaximum principle and a second-order necessary optimal-ity condition in the form of an integral inequality whichextends some earlier known results to the case of stronglocal minimizers.
Daniela TononIMJ UPMC Paris [email protected]
Helene FrankowskaCNRS and IMJ-PRG UPMC Paris [email protected]
Daniel [email protected]
MS44
Toward Massive Deployment of Power Electronicsin Future Electric Energy Systems: Modeling andControl Challenges and Opportunities
In this talk we pose the problem of fast digital control de-sign for changing electric power systems. The underlyingmodeling, placing and tuning of minimal number of fastnonlinear digital controllers in both microgrids and EHVpower plants is discussed in light of the state-of-the-artin nonlinear control for general large scale dynamical sys-tems. We combine the rich structure of the underlyingpower system with general methods on the way to a sys-tematic design framework.
Marija IlicCarnegie Mellon [email protected]
MS44
Balanced Control Strategies for HeterogeneousBattery Systems for Smart Grid Support
This paper introduces new balanced charge/discharge con-trol strategies that distribute charge or discharge currentsproperly so that during operations battery pack balancing
112 CT15 Abstracts
is continuously maintained. The strategies are targetedfor serially interconnected heterogeneous battery systemsto be used for power grid support. SOC-based balancedcharge/discharge strategies are developed. Their conver-gence properties are rigorously established, and simulationexamples demonstrate their convergence behavior underdifferent charging current profiles. Also, robustness againstparameter estimation errors is discussed.
Michael P. PolisOakland [email protected]
Le Yi Wang, Caisheng WangWayne State [email protected], [email protected]
George YinWayne State UniversityDepartment of [email protected]
Feng LinWayne State [email protected]
MS44
Is Consumer-Based Integration of Renewable andStorage Good for Consumers?
Two models of renewable integration and the use of stor-age in distribution networks are considered. The first is acentralized utility-based model in which the utility ownsthe renewable generation as part of its portfolio of energyresources. The second is a decentralized consumer-basedmodel in which each consumer owns the renewable gener-ation and is allowed to sell surplus electricity back to theutility in a net-metering setting. Similar models for storageare also considered: the utility owned and operated stor-age vs. consumer owned and operated one. The essentialquestion is whether consumer owned and operated renew-able generation or storage ultimately benefits the consumerunder a profit regulated monopoly.
Liyan Jia, Lang TongCornell [email protected], [email protected]
MS44
Exploiting Energy Storage for Integration of Re-newables in Low Voltage Networks
Electricity networks have witnessed the outgrowth ofa huge number of uncertainty sources and constraints,mainly due to the rising amount of renewable generationand the increased sensitivity of customers to quality ofservice. We investigate optimal sizing and placement ofan energy storage to address both over- and under-voltageproblems in distribution networks. An optimal power flowis formulated where the total storage budget is minimizedsubject to power flow equations, energy storage dynamicsand voltage quality constraints. A convex relaxation ap-proach is exploited to provide a suboptimal solution.
Antonio GiannitrapaniUniversita’ di Siena, [email protected]
Simone Paoletti
Universita di Siena, Via Roma 5653100 Siena (Italy)[email protected]
Antonio VicinoUniversita di [email protected]
Donato ZarrilliUniversita di SienaDip. Ingegneria dell’Informazione e Scienze [email protected]
MS45
An Optimal Junction Solver for Traffic Flow
Abstract not available.
Annalisa CesaroniDipartimento di MatematicaUniversita di [email protected]
MS45
On the Attainable Set for Scalar Conservation Lawsand Its Application
Abstract not available.
Shyam Sundar GhoshalGSSI, Gran Sasso Science InstituteL’Aquila, [email protected]
MS45
On the Uniform Controllability of the One-Dimensional Transport-Diffusion Equation in theVanishing Viscosity Limit
Abstract not available.
Pierre LissyParis-Dauphine UniversityParis, [email protected]
MS45
Exact Boundary Controllability of Nodal Profile forQuasilinear Wave Equations in a Planar Tree-LikeNetwork of Strings
Abstract not available.
Ke WangParis-Dauphine UniversityParis, [email protected]
MS46
Estimation of a Gaseous Release into the Atmo-sphere Using An Unmanned Aerial Vehicle
We propose a scheme based on controls and computationalfluid dynamics to provide real-time estimates of the gasconcentration released in the atmosphere from a movingsource. The concentration is estimated numerically usingan unmanned aerial vehicle equipped with a gas sensor.
CT15 Abstracts 113
The performance-based motion control of the sensing aerialvehicle is integrated into the performance state estimationscheme. The resulting guidance scheme couples the vehiclemotion to the estimator performance.
Nikolaos GatsonisWorcester Polytechnic [email protected]
Michael A. DemetriouWorcester Polytechnic [email protected]
Tatiana EgorovaWorcester Polytechnic [email protected]
MS46
LQG Controller Equivalent to the Control by In-terconnection for Infinite Dimensional Port Hamil-tonian System
This paper proposes a method that combines LQG controldesign and structure preserving model reduction for thecontrol of infinite dimensional port Hamiltonian systems(IDPHS). A modified LQG controller design equivalent tocontrol of IDPHS by interconnection is first proposed. Themethod of Petrov-Galerkin is then used to approximate thebalanced realization of the IDPHS by a finite dimensionalport Hamiltonian system and to provide the associated re-duced order LQG controller.
Yongxin Wu, Boussad HamrounLAGEP, University Lyon1, 43 Bvd du 11 Nov. 191869100 [email protected], [email protected]
Yann Le GorrecFEMTO-ST AS2M, [email protected]
Bernard MaschkeLAGEP, Universite Claude Bernard - Lyon 1Lyon, [email protected]
MS46
Robustness of Nonlinear Optimal Regulator for Re-duced Distributed Parameter System
This paper proposes an evaluation index of robustness todisturbances for distributed parameter systems with non-linear optimal feedback designed by the stable manifoldmethod that is a numerical calculation method of Hamil-ton Jacobi equations, and the POD-Galerkin method thatis a finite dimensional reduction method. We state a robustcontrol problem described by POD bases and disturbances.Then, we show that the problem can be formulated as ageneralized eigenvalue problem.
Gou NishidaIntelligent and Control Systems Laboratory, Departmentof [email protected]
Noboru SakamotoNanzan University
MS47
Computing Reachable Sets by Distance Functionsand Solvers for Optimal Control Problems
Reachable sets of nonlinear state-constrained control prob-lems are calculated by solving parametric optimal controlproblems with a suitable OCP solver. Here, the feasible setequals the reachable set and the optimal value coincideswith the distance function of a grid point to the reach-able set. A lower-dimensional projected reachable set ofa single-track model for collision avoidance is computed.Possible speedups of the algorithm by the piecewise lin-ear interpolated distance function and parallelization aredemonstrated.
Robert BaierDepartment of Mathematics, University of [email protected]
MS47
A Dual Model/Artificial Neural Network Frame-work for Privacy Analysis in Traffic MonitoringSystems
Most large-scale traffic information systems rely on a com-bination of fixed sensors (e.g. loop detectors) and usergenerated data, the latter in the form of probe traces sentby GPS devices on vehicles. While this type of data is rel-atively inexpensive to gather, it can pose multiple privacyrisks, even if the location tracks are anonymous. We pro-pose a new framework for analyzing a variety of privacyproblems arising in transportation systems.
Edward CanepaKing Abdullah University of Science and TechnologyDepartment of Electrical [email protected]
Christian ClaudelKing Abdullah University of Science and Technolgy(KAUST)Electrical Engineering and Mechanical [email protected]
MS47
Hamilton-Jacobi Approach for Second Order Traf-fic Flow Models
While being simple and tractable, the first order LWRmodel does not reproduce certain meaningful traffic phe-nomenon. Second order traffic flow models have been de-veloped to fill this gap. In this talk, I will focus on theGeneric Second Order Model (GSOM) family which em-beds lots of these models. Recasting the GSOM in La-grangian coordinates allows us to use the Hamilton-Jacobiframework and to deduce a Lax-Hopf type formula whichis helpful for numerical resolution.
Guillaume CostesequeInria Sophia Antipolis - [email protected]
MS47
Robust Control Problems - from the Perspective of
114 CT15 Abstracts
Evolution Equations for Sets
In ”robust” control problem, two types of controls occurand, the user can choose only one of them whereas the otherone is not known exactly (i.e., uncertainty). Whenever allpossibilities for the second control are considered simulta-neously, states should be described as sets. We discuss anextension of differential equations to set-valued states. Itis illustrated by examples and their numerical solutions. Iteven lays the analytical foundations for control problemswith state constraints.
Thomas LorenzRheinMain University of Applied SciencesApplied [email protected]
MS48
Linear Stochastic Control with State and ControlDependent Noise
The control of a linear stochastic system with stochasticcoefficients, linear state and control dependent noise, anda quadratic cost is formulated and solved. A stochastic Ric-cati equation is used to obtain the explicit optimal controlin a direct way using a decomposition of submartingalesfrom the running cost and the Lagrangian Grassmannianfor the control problem. This problem have been consid-ered by some others using different approaches.
Tyrone E. DuncanUniversity of KansasDepartment of [email protected]
Bozenna Pasik-DuncanUniversity of [email protected]
MS48
Hidden Markov Change Point Estimation
A hidden Markov model is considered where the dynamicsof the hidden process change at a random ‘change point’ T.In principle this gives rise to a non-linear filter but closedform recursive estimates are obtained for the conditionaldistribution of the hidden process and of T.
Robert J. ElliottUniversity of [email protected]
Sebastian ElliottElliott Stochastics [email protected]
MS48
On Cooling of Stochastic Oscillators
Active control of micro/macro mechanical systems to re-duce thermal noise is implemented in atomic force mi-croscopy, polymer dynamics and gravitational wave detec-tors. For a system of nonlinear stochastic oscillators, weconsider the problem of feedback controlling the system ef-ficiently to a desired steady state corresponding to lowerthermal noise both asymptotically and in finite time . Thesolution (in closed-form in the Gaussian case) involves ex-tending and adapting the classical theory of Schroedinger
bridges.
Yongxin Chen, Tryphon T. GeorgiouUniversity of [email protected], [email protected]
Michele PavonUniversity of [email protected]
MS48
On some Connections between Information Theory,Nonlinear Estimation and Statistical Mechanics
In this talk I discuss the connections that exist betweenNonlinear Filtering for Diffusion Processes, the VariationalCharacterization of Gibbs Measures and Information-theoretic characterization of optimality of nonlinear esti-mators . It relies on T.E. Duncans important work onthe computation of Mutual Information for Diffusion Pro-cesses. I discuss also the role of Information Theory in thecontext of the Separation Theorem of Stochastic Control,Dual Control and Self Tuning Regulators
Sanjoy K. [email protected]
MS49
Homogenization Results for Hamilton-JacobiEquations on Networks
Abstract not available.
Cyril ImbertParis-Dauphine [email protected]
MS49
Singular Perturbation of Optimal Control Prob-lems on Periodic Multi-Domains
In this talk we consider the singular perturbation of anoptimal control problem in which the controlled system in-volves a fast and a slow variables. The fast variable livesin periodic multi-domains. The problem can be reformu-lated as a Hamilton-Jacobi-Bellman (HJB) equation, whilethe geometric singularity of the multi-domains leads to thediscontinuity of the Hamiltonian. Under a controllabilityassumption on the fast variable, the limit problem has beenanalyzed and the associated HJB equation has been ob-tained. This equation describes the limit behavior of thevalue function of the perturbed problem when the scale ofperiodicity tends to 0.
Zhiping RaoRICAM, Austrian Academy of [email protected]
Nicolas ForcadelINSA de [email protected]
MS49
The Hamilton Jacobi Equation for Optimal Control
CT15 Abstracts 115
Problems with State Constraints
We discuss conditions under which the value function for astate-constrained optimal control problem can be charac-terized as the unique generalized solution of the HamiltonJacobi equation. Special attention is given the interplaybetween the validity of this characterization and systemtheoretic properties (controllability and monotonicity) ofthe underlying dynamic constraint and the regularity ofthe data, and new classes of problems are identified, forwhich the characterization is possible.
Richard B. VinterImperial College, Exhibition Road, London SW7 2AZ, [email protected]
MS49
Optimal Control Problems on Generalized Net-works
This talk concerns some optimal control problems on d-dimensional networks. We will present a new charac-terization of the value function as solution to a systemof Hamilton- Jacobi- Bellman equations with appropriatejunction conditions. This result doesn’t require the usualcontrollability condition on the junction and it still holdswhen the value function is discontinuous.
Hasnaa ZidaniENSTA ParisTech, INRIA [email protected]
Cristopher HermosillaENSTA [email protected]
MS50
Stabilisation of Dynamical Systems Subject toSwitching and Two Time Scale Phenomena
This talk is dedicated to the problem of stability analysisand control design of singularly perturbed switched sys-tems. The problem of norms computations such as H2 andH infinity norms is presented and the generalization to thecase of switching and switched singularly perturbed sys-tems is discussed. The talk focuses on open problems forthis class of hybrid systems. We illustrate the differentnotions and properties discussed in this presentation usingnumerical examples.
Jamal DaafouzCRAN, Universite de [email protected]
MS50
Commutators, Robustness, and Stability ofSwitched Linear Systems
The subject of this work is stability analysis of switchedlinear systems, described by a family of continuous-timelinear dynamical systems and a rule that orchestrates theswitching between them. There are well-known resultsstating that stability is preserved under arbitrary switchingprovided that certain commutation relations hold betweenthe matrices being switched, in particular, if the matricescommute or generate a nilpotent or solvable Lie algebra.The present works aims at obtaining stability conditionsalong these lines which are robust with respect to suffi-ciently small perturbations of the system data (such per-
turbations destroy exact commutatitivy). This leads di-rectly to questions like when are almost commuting matri-ces nearly commuting, i.e., does smallness of commutatorsimply proximity to commuting matrices? When the an-swer is yes, existence of Lyapunov functions coupled witha perturbation analysis can be used to show stability andto estimate allowable deviations of the commutators fromzero. Similar results can be derived for nilpotent or solv-able Lie algebras. Among a number of available resultson almost commuting vs. nearly commuting matrices, wework with the �Lojasiewicz inequality which lower-boundsthe value of a polynomial in terms of the distance to itsset of zeros. Applied in our framework, the �Lojasiewiczinequality and other related results allow us to obtain ro-bust versions of Lie-algebraic stability criteria for switchedlinear systems.
Daniel LiberzonDepartment of Electrical and Computer EngineeringUniversity of [email protected]
Yuliy BaryshnikovUniversity of Illinois at UrbanaChampaignDepartment of [email protected]
MS50
Stability of Linear Difference Equations withSwitching Parameters and Applications to Trans-port and Wave Propagation on Networks
This talk addresses the stability of linear difference equa-tions of the form
x(t) =N∑i=1
Ai(t)x(t− Li), x(t) ∈ Cd,
for positive delays Li. When the matrices Ai are time-independent, the corresponding autonomous system canbe analyzed by Laplace transform methods leading to thewell-known Silkowski’s criterion, but this technique fails toapply to the non-autonomous case. Using an explicit for-mula for solutions, we get a stability criterion for the non-autonomous system. When applied to the case of switchingmatrices Ai(·) subject to arbitrary switching signals, oneobtains a criterion in terms of a generalized joint spectralradius, which extends Silkowski’s criterion. Correspondingstability criteria for transport and wave propagation onnetworks with variable coefficients are derived by express-ing these systems as difference equations. In particular, weshow that the wave equation on a network with arbitrar-ily switching damping at external vertices is exponentiallystable if and only if the network is a tree and the dampingis bounded away from zero at all external vertices but one.
Yacine ChitourUniv. Paris Sud & [email protected]
Guilherme Mazanti
CMAP, Ecole [email protected]
Mario SigalottiINRIA, Centre de Recherche Nancy - Grand Est
116 CT15 Abstracts
MS50
Analysis of the Limit Sets of Switched Systems
We consider switched systems, both linear and non linear,whose trajectories are bounded by a weak Lyapunov func-tion V . We investigate the convergence of the trajectoriestowards two different locus according to the class of switch-ing laws considered. For each vector field fi we considerthe set Ki where the derivative of V along fi vanishes, andthe subset Ni of Ki invariant under fi. The limit sets forinputs with (roughly speaking) dwell-time are contained inthe union of the Ni, and the limit sets for general inputs arecontained in the union of the Ki. Consequently the asymp-totic properties of such systems are entirely encrypted inthe geometry of the Ni’s, or the Ki’s, according to thekind of inputs we consider. In the case of two asymptot-ically stable linear vector fields the asymptotic propertiesare also related to the observabiliy properties of a relatedsystem, generally much smaller. To finish we show that asystem which is asymptotically stable for dwell-time inputsbut not GUAS possesses trajectories that converge to theorigin as slowly as wanted, but that with a fixed dwell-timean exponential convergence rate is obtained. These last tworesults can be partially extended to non linear systems.
Saıd Naciri, Philippe JouanLMRS, Universite de [email protected], [email protected]
MS51
Time-Zero Controllability and Density of Orbits forQuantum Systems
For a bilinear finite dimensional closed quantum systemon the sphere S2n−1 we study under which conditions wecan control the system in an arbitrary small time. Thisstudy is based on representation theory of su(n) and onthe equivalence between approximate and exact control-lability for finite dimensional quantum systems, that hasbeen recently proved. One interesting fact is that, withoutadditional hypotheses, this result does not extend to theSchroedinger equation as a PDEs.
Ugo BoscainCNRS, CMAP Ecole [email protected]
Mario SigalottiINRIA, Centre de Recherche Nancy - Grand [email protected]
MS51
Theoretical and Numerical Aspects in Control ofOpen Quantum Systems
We address the problem of controllability of quantum sys-tems interacting with an engineered environment,with dy-namics described by a non-Markowian master equation.The manipulations of the dynamics is realized with botha laser field and a tailored non-equilibrium, and generallytime-dependent, state of the surrounding environment. Liealgebra theory is used to characterize the structures of thereachable state sets and to prove controllability. In order toensure certain physical properties of the quantum systemsoptimal control problem are formulated and solved using
an optimization algorithm. The results are supported byexamples.
Andreea GrigoriuLaboratoire Jacques-Louis LionsUniversite [email protected]
MS51
Sparse Time-Frequency Control of Quantum Sys-tems
We propose an optimal control framework to generate con-trol fields with a very simple time-frequency structure. Weachieve this by using cost functionals in the time-frequencyplane that enhance sparsity in frequencies and smoothnessin time. Mathematically this is realized by working in aspace of function-valued measures. I will give an outlineof the proposed control framework, will discuss first orderoptimality conditions and present numerical results for anexample from molecular control.
Felix HennekeTechnische Universitat MunchenCenter for [email protected]
Gero FrieseckeCentre for Mathematical SciencesTechnische Universitat Munchen, [email protected]
Karl KunischKarl-Franzens University GrazInstitute of Mathematics and Scientific [email protected]
MS51
Quantum Filtering and Parameter Estimation
Open quantum systems subject to measurement back-action and decoherence are described by stochastic masterequations. We present here a quantum filtering process,based on the measurement outcomes, to discriminate be-tween different parameter values and we prove its stability.Numerical implementations on simulated and experimen-tal data illustrate the interest of this estimation method.
Pierre SixCentre Automatiques et Systemes, [email protected]
MS52
Semidefinite Programming for Stochastic Control
We formulate constrained stochastic control problem as aninfinite dimensional linear program. We use semidefiniteprogramming (SDP) to approximate the primal and duallinear program. As such, we approximate the value func-tion of the optimal control problem from the primal linearprogram and we approximate the optimal policy from thedual linear program. We discuss computational tractabil-ity of the SDP algorithm. Furthermore, we illustrate theapproach on a few benchmark case studies.
Maryam KamgarpourETH Zurich
CT15 Abstracts 117
MS52
Inference and Stochastic Optimal Control
The path integral control theory describes a class of controlproblems whose solution can be computed as an inferencecomputation. The efficiency of the inference computationis related to the proximity of the sampling control to theoptimal control. This forms the basis of a novel adaptivesampling procedure. The adaptive sampling procedure canbe used to compute optimal controls as well as to accelerateother Monte Carlo computations.
Bert KappenSNN Machine Learning GroupRadboud University [email protected]
MS52
Randomized Methods for Stochastic ConstrainedControl
We address finite-horizon control for a stochastic linear sys-tem subject to constraints on control input and state. Acontrol design methodology is proposed where the trade-off between control cost minimization and state constraintssatisfaction is decided by introducing appropriate chance-constrained problems depending on some parameter tobe tuned.From an algorithm viewpoint, a computationallytractable randomized approach is proposed to provide anapproximate solution with probabilistic guarantees aboutits feasibility for the original chance-constrained problem.
Maria PrandiniDipartimento di Elettronica e InformazionePolitecnico di [email protected]
MS52
Learning in Mean-Field-Type Teams and Games
We consider mean-field-type stochastic games with con-tinuous action spaces. We show that one can achievetarget actions as risk-sensitive team optima and equi-libria without knowing the underlying payoff functions.Furthermore, under fairly general settings on Brownian-driven state dynamics, one can efficiently approximate risk-sensitive mean-field optima in (expected) Hamiltonian po-tential games and in games with monotone sub-gradient(expected) payoffs. We then focus on speedup model-freelearning techniques. Our result builds upon various un-certainty quantification and variance reduction techniques.
Hamidou TembineLSS, CNRS-Supelec-Univ. Paris Sud, [email protected]
MS53
Symbolic Regression for the Modeling of ControlFunctions
Abstract not available.
Markus W AbelAmbrosys GmbH
MS53
Low-Complexity Stochastic Modeling of TurbulentFlows
Second-order statistics of turbulent flows can be obtainedeither experimentally or via direct numerical simulations.Due to experimental or numerical limitations it is often thecase that only partial flow statistics are reliably known.Thus, it is of interest to complete the statistical signatureof the flow field in a way that is consistent with the knowndynamics. We formulate a convex optimization problemthat addresses this challenge.
Armin ZareUniversity of [email protected]
Mihailo R. JovanovicElectrical and Computer EngineeringUniversity of [email protected]
Tryphon T. GeorgiouUniversity of [email protected]
MS53
Crom-Based Closed-Loop Control of a CanonicalSeparated Flow
Abstract not available.
Eurika KaiserInstitute PPRIME, [email protected]
MS53
Closed-Loop Turbulence Control Using MachineLearning
Abstract not available.
Bernd R. NoackInstitut PPRIME, [email protected]
MS54
Practical Advances in Data-Driven Koopman Spec-tral Analysis and the Dynamic Mode Decomposi-tion
The dynamic mode decomposition (DMD) is a techniquefor approximating the Koopman operator and extractingdynamical descriptions of a system from observed snap-shot data. Here, we present several variations of DMD thatfacilitate Koopman spectral analysis in practical contextsinvolving large, streaming, and/or noisy datasets. We alsoshow that extending DMD to include additional observ-ables can yield more authentic Koopman-based descrip-tions. Each DMD method will be demonstrated on numer-ical and experimental fluids data.
Maziar S. HematiPrinceton [email protected]
118 CT15 Abstracts
Matthew O. WilliamsProgram in Applied and Computational MathematicsPrinceton [email protected]
Scott DawsonPrinceton [email protected]
Clarence RowleyPrinceton UniversityDepartment of Mechanical and Aerospace [email protected]
MS54
Application of the Koopman Operator to Differen-tial Positivity
Differential positive systems are systems that infinitesi-mally contract a given cone field. Under mild assump-tions, their solutions asymptotically converge to a one-dimensional attractor, which must be a limit cycle in theabsence of fixed points in the limit set. We use the spec-tral properties of the Koopman operator to show a conversetheorem for differential positivity: every system is differ-entially positive in the basin of attraction of a hyperboliclimit cycle.
Alexandre MauroyUniversity of [email protected]
Fulvio ForniUniversity of [email protected]
Rodolphe SepulchreUniversity of CambridgeCambridge, [email protected]
MS54
Koopman Operator Theory for Dynamical Systemsand Control Practice
We discuss current theory and practice of applications ofKoopman operator methods in dynamical systems and con-trol and its relationship with computational methods. Theapproach has recently been extended to associate geomet-rical objects such as isochrons and isostables - using levelsets of Koopman eigenfunctions. We will also discuss therelationship between numerical methods such as DynamicMode Decomposition and Koopman Mode Decomposition,and extensions of theory to stability of nonlinear systemsand control.
Igor MezicUniversity of California, Santa [email protected]
MS54
Koopman Spectral Analysis for Estimation, Fore-casting and Detection
The dynamics of observables or system outputs definedon state space of a (nonlinear) dynamical system evolvelinearly in time in Koopman spectral representation. Weexploit this property to construct a linear time invariant
system for output evolution, and thereby develop a frame-work for exploiting linear system estimation, detection andcontrol theory for nonlinear systems. We demonstrate ourframework for modeling and forecasting of time series data,estimating missing sensor data, and anomaly detection.
Amit SuranaSystem Dynamics and OptimizationUnited Tecnologies Research Center (UTRC)[email protected]
Andrzej BanaszukUnited Technologies Research [email protected]
MS55
Pontryagin Maximum Principle for Control Sys-tems on Infinite-Dimensional Manifolds
We present a proof of Pontryagin’s Maximum Principlefor control problems on infinite-dimensional Banach man-ifolds. Our proof makes use of techniques of nonsmoothanalysis, demonstrating their utility even for smooth prob-lems. In addition, we introduce the technique of La-grangian charts for geometric problems of dynamic opti-mization and discuss an interesting constraint qualification.Failure of this constraint qualification implies the abnormalcase of the Maximum Principle, while its presence allowsremoval of endpoint constraints through penalization.
Robert KipkaQueen’s [email protected]
Yuri LedyaevWestern Michigan [email protected]
MS55
A Maximum Principle for Implicit and DAE Sys-tems
The presentation focuses on a nonsmooth maximum prin-ciple for problems involving implicit control systems. Thestarting point is a known result in Optimal Control withMixed Constraints by [Clarke et all, in SIAM J. ControlOptimization, 2010]. We first extend this result to coversome situations where less regularity is assumed. We thenillustrate the special features of this result, in the smoothand nonsmooth case, with some simple examples. In par-ticular, we apply it to some special cases, namely controlsystems involving semi-explicit differential algebraic equa-tions.
Maria doRosario de PinhoUniversity of PortoFaculdade de [email protected]
Igor KornienkoUniversidade do [email protected]
MS55
Necessary and Sufficient Conditions for Invarianceof Time Delayed Systems
In this talk we will present necessary and sufficient condi-
CT15 Abstracts 119
tions of invariance for time delayed systems parametrizedby differential inclusions. Weak invariance properties willbe presented as well as our progress towards character-izing strong invariance in this setting. In addition, wewill explain the effects of our results towards developinga Hamilton-Jacobi theory for the minimal time problemunder time delayed constraints.
Norma Ortiz-RobinsonVirginia Commonwealth [email protected]
MS55
An Adaptive Mesh Refinement Algorithm for Op-timal Control Problems
When solving nonlinear optimal control problems via di-rect methods, the time interval is discretized and, most fre-quently, equidistant-spacing meshes are used. However, toachieve the desired accuracy in nonlinear problems, thesemeshes might have a large number of nodes which, in somecases, prevent the optimizers to find an adequate solution.We propose an adaptive time-mesh refinement algorithm,considering different levels of refinement and several meshrefinement criteria. In particular, the local error of the ad-joint multipliers is chosen as a refinement criterion. Thiserror can be computed efficiently by comparing the solu-tion to a linear differential equation system – the adjointequation of the maximum principle – with the numericallyobtained dual variables. Finally, we extend this refinementalgorithm to solve a sequence of optimal control problemsin a Model Predictive Control (MPC) scheme. We applythe developed scheme to a problem involving manoeuvresof nonholonomic vehicles with state constraints. We showthat the refinement technique leads to numerical resultswith higher accuracy and yet with lower overall compu-tational time, when compared with alternative methods.
Fernando A. Fontes, Luis Tiago PaivaUniversidade do [email protected], [email protected]
MS56
Null Controllability of Grushin and KolmogorovEquations
From the controllability viewpoint, degenerate parabolicpartial differential equations have interesting features. De-pending on the strength of the degeneracy, null control-lability may hold or not; it may also require a geometriccondition and a positive minimal time. In this talk, proofswill be explained on prototype equations of Grushin andKolmogorov type.
Karine BeauchardENS Rennes, [email protected]
MS56
A Control Condition for a Weak Harnack Inequal-ity
We introduce a condition allowing to get a weak Har-nack inequality for nonnegative solutions to linear sec-ond order degenerate elliptic equations of X-elliptic type.Roughly speaking, our condition requires that the Eu-clidean balls of small radius are representable by means ofX-controllable almost exponential maps. Our results apply
to Δλ-Laplacians (e.g., Grushin-type operators) as well asto Elliptic Operators on Lie groups (e.g., Sub-Laplacianson Carnot groups).
Alessia KogojUniversita di Bologna, [email protected]
MS56
The Minimal Control Time for DegenerateParabolic Equations of Grushin Type
We control degenerate parabolic equations of Grushin type:∂2xx + V (x)∂2
yy on the rectangle (x, y) ∈ (−1, 1) × (0, 1),where V ≥ 0 vanishes only on the line x = 0. Our inputis a source term supported on parallel strips on each sideof this line. Previous works with V (x) = |x|2γ proved thatnull controllability fails for γ > 2, holds arbitrarily fast forγ ∈ (0, 1), and requires a positive minimal time for γ = 1.We prove that this time is the distance of the control stripsfrom the degeneracy line x = 0 computed using the Agmonmetric V (x)dx2 instead of dx2.
Luc MillerUniversite Paris Ouest Nanterre La [email protected]
MS56
Intrinsic Random Walks and Diffusion in Sub-Riemannian Geometry
In Riemannian geometry, a possible definition of theLaplace-Beltrami operator is as the generator of the diffu-sion obtained as the limit of geodesic random walks. Thiscoincides with the usual divergence of the gradient. Wediscuss how to extend these definitions in sub-Riemanniangeometry, where it is not clear what is an intrinsic randomwalk and what is an intrinsic volume. Joint work with U.Boscain and R. Neel.
Luca RizziCMAP, Ecole Polytechnique, [email protected]
MS57
L2-Induced Gains of Switched Linear Control Sys-tems
In this talk, we present results on L2-gain issues relatedto linear control switched systems. For that purpose, weintroduce several concepts of extremal norms in the spiritof the well-known Barabanov norm. Joint work with P.Mason and M. Sigalotti.
Yacine ChitourUniv. Paris Sud & [email protected]
MS57
A Hamilton-Jacobi Approach to Barabanov Normsof Positive Linear Systems
We study switched positive linear systems, and show thatfor these systems, Barabanov norms are equivalent toweak-KAM solutions of a class of Hamilton-Jacobi PDE.Then, we discuss the application of PDE or semigroupmethods to establish the existence of Barabanov norms,
120 CT15 Abstracts
exploiting controllability conditions or contraction prop-erties in Hilbert’s projective metric. We investigate theasymptotic behavior of optimal trajectories of the associ-ated control problem.
Vincent CalvezUnite de Mathematiques Pures et AppliqueesEcole Normale Superieure de [email protected]
Pierre GabrielUniversite de Versailles [email protected]
Stephane GaubertINRIA and CMAP, Ecole [email protected]
MS57
Resonance of Extremal Norms, Marginal Instabil-ity, and Sublinear Growth
We analyse the marginal Instability of switching linear sys-tems, both in continuous and discrete time. That is, weare interested in situations where the system is not sta-ble, but all trajectories grow less than exponentially. Wedisprove two recent conjectures of Chitour, Mason, andSigalotti (2012) stating that for generic systems, the res-onance is sufficient for marginal instability and for poly-nomial growth of the trajectories. We provide an efficientcharacterization of marginal instability under some mildassumptions on the system. Finally, we analyze possibletypes of fastest asymptotic growth of trajectories. An ex-ample of a marginally unstable pair of matrices with sub-linear growth is given. This is joint work with V. Protasov.
Raphael JungersMassachusetts Institute of TechnologyLaboratory for Information and Decision [email protected]
MS57
Extremal Norms and Linearization Principles forMonotone Systems
Extremal norms characterize the exponential growth ratefor several classes of systems that model time-varyinguncertainty, such as discrete or differential inclusions,or ot use a different terminology switched disrete-time,continuous-time or differential-algebraic systems. For lin-ear inclusions that leave a cone invariant it can be shownunder a mild irreducibility condition that extremal normsexist that respect the order induced by the cone, i.e. theextremal norms are monotone. On the one hand this pro-vides a new criterion for the existence of extremal norms,which as corollaries provides new insight in robustness, sta-bility and sensitivity results that have known proofs relyingon the properties of extremal norms. A further applicationof interest is particular to the case of cone-invariance. Lin-ear inclusions that leave a cone invariant occur naturally asthe linearization at fixed point of differentiable monotoneinclusions. It turns out that the use of extremal normsin the local stability analysis at fixed points yields sharpstability estimates for monotone inclusions, which extendclassical results available for time-invariant monotone dy-
namical systems.
Oliver MasonNUI Maynooth, [email protected]
Fabian WirthUniversity of [email protected]
MS58
An Optimal Device Placement Approach for SemiLinear Pde Systems over Irregular Spatial Domains
A methodology is presented for placing actuating and sens-ing devices with respect to power criteria for semi-linearPDE process systems over irregular spatial domains. ThePDE is discretized using nonlinear Galerkin’s method withstatistically-derived basis functions, Laplace transformsand singular perturbation arguments. A non-convex NLPis then formulated and solved using an interior point globalsearch algorithm. The methodology is illustrated on theplacement of sensing devices for an environmental process.
Antonios ArmaouDepartment of Chemical EngineeringThe Pennsylvania State [email protected]
Michael A. DemetriouWorcester Polytechnic [email protected]
MS58
Networked Control of Spatially Distributed Sys-tems Using Quantized and Delayed Sensing andActuation
This work considers the stabilization of spatially-distributed systems with low-order dynamics, using net-worked sensors and actuators subject to quantization andcommunication delays. A finite-dimensional model-basedcontroller that explicitly compensates for communicationdisruptions and delays is designed, and its closed-loop sta-bility properties under sensor/actuator quantization arecharacterized using Lyapunov techniques. This character-ization is used to develop sensor/actuator reconfigurationstrategies that mitigate the impact of delays and quanti-zation on performance. The results are illustrated throughnumerical simulations.
Nael H. El-FarraUniversity of California, DavisDepartment of Chemical Engineering and [email protected]
MS58
Sensor Location in Feedback Stabilization of theBoussinesq Equations
In this talk, we discuss the problem of sensor placementin feedback stabilization of a thermal fluid described bythe Boussinesq equations. This problem is motivated bythe design and operation of low energy consumption build-ings. We apply the MinMax compensator design to obtaina reduced-order observer for state estimation based on the
CT15 Abstracts 121
geometric structure of feedback functional gains. A two di-mensional problem is employed to illustrate the theoreticaland numerical results and to demonstrate the feasibility ofthis method.
Weiwei HuUniversity of Southern [email protected]
MS58
Shape Optimization for Second-Order Systems
Modern materials mean that it is possible to provide pas-sive damping for vibrations. Consider choosing viscousdamping in abstract second-order systems; that is choosed(x) in
w(x, t) + Aow(x, t) + d(x)Iw(x, t) = 0
where Ao is a non-negative self-adjoint operator. The moti-vating example is a vibrating beam or string where patchesare placed to increase viscous damping. Optimal dampingin a vibrating string has been studied by many researchers;for instance Cox and Zuazua (1994), Fahroo and Ito (1997),Hebrard and Henrot (2005), Privat et al (2013). The ap-proach of Morris (2011) is extended to obtain new results,which also apply to first order systems. It is shown thatminimization of a quadratic cost functional is appropriatefor maximization of the decay rate. The existence of anoptimal actuator location depends on the continuity of thegenerator with respect to d. The results are illustrated withsimulations.
Kirsten Morris, Ambroise VestDept. of Applied MathematicsUniversity of [email protected], [email protected]
MS59
Towards Moment Matching of a Perturbed WavePDE
Finite-dimensional approximations of partial differentialequations are used not only for simulation, but also forcontroller design. The model reduction technique we use isthe so-called time-domain moment matching method. Theidea is that the steady-state response of the approximantwhen excited by some specific input signal matches thesteady-state response of the given model, when excited bythe same input. The result of applying this method is afamily of parameterized approximations which contains awide variety of models suitable for different goals. We aregoing to exploit this asset for boundary control systemsand explore it for a particular fractional system, namely aperturbed wave equation.
Orest IftimeDepartment of Economics and EconometricsUniversity of [email protected]
Tudor IonescuUniversity of SheffieldDepartmen of Automatic Control and [email protected]
Denis MatignonISAE-Supaero, University of Toulouse
MS59
Well-Posedness of Hyperbolic Partial DifferentialEquations on the Semiaxis
Hyperbolic partial differential equations on the semiaxisare studied. This class of systems includes models of beamsand waves as well as the transport equation and networks ofnon-homogeneous transmission lines on the semiaxes. Themain result of this talk is a simple test for C0-semigroupgeneration in terms of the boundary conditions at the pointzero. The results are illustrated with several examples.
Birgit JacobUniversitat Wuppertal, [email protected]
Sven-Ake WegnerUniversity of [email protected]
MS59
Strong Stabilization of the SCOLE Model using aTuned Mass Damper
We study the vibration reduction of the non-uniformSCOLE (NASA Spacecraft Control Laboratory Experi-ment) model representing a vertical beam clamped at thebottom, with a rigid body having a large mass on top, us-ing a Tuned Mass Damper (TMD). The TMD is a heavytrolley mounted on top of the rigid body, connected to therigid body via a spring and a damper. Such an arrange-ment is used to stabilize tall buildings. Using our recentwell-posedness and strong stabilization results for coupledimpedance passive linear time-invariant systems (possiblyinfinite-dimensional), we show the following: The SCOLEsystem with the trolley is well-posed and regular on theenergy state space with the force or torque acting on therigid body as input and with the speed or angular velocityof the rigid body as output, and this system is stronglystable on the energy state space.
Xiaowei ZhaoSchool of EngineeringUniversity of [email protected]
George WeissSchool of Electrical EngineeringTel Aviv [email protected]
MS59
Waves: Observation, Control and Numerics
We present a recent result on numerical approximation ofboundary-controlled wave equations. When the wave equa-tion is discretized, most numerical schemes produce highfrequency wave packets with null group velocity that donot reach the boundary, and accordingly cannot be con-trolled. We construct a suitable non-uniform grid, suchthat controllability is ensured uniformly on the mesh sizeparameter. This allows ensuring the convergence of the nu-merical approximations of the boundary controls withoutadded filtering mechanisms.
Enrique Zuazua
122 CT15 Abstracts
Ikerbasque & Basque Center for Applied Mathematics([email protected]
MS59
Exponential Stabilization of Boundary ControlledLinear Port Hamiltonian Systems with Non-linearDynamic Control
Exponential stability of boundary controlled port-Hamiltonian systems defined on a one-dimensional spatialdomain with non-linear dynamic boundary controller is ad-dressed. For a finite-dimensional controller it is shown thatthe closed-loop system possesses unique solutions, and thatexponential stability can be obtained. This result followsby regarding the closed-loop system as a linear boundarycontrol system subject to a Lipschitz continuous non-linearperturbation at its boundary. By estimating the decay ofenergy exponential stability is proved.
Hans ZwartDepartment of Applied MathematicsUniversity of [email protected]
Yann Le Gorrec, Hector RamirezFEMTO-ST AS2M, [email protected], [email protected]
MS60
Homogenization of a Precipitation-dissolutionModel in a Porous Medium
We employ homogenization techniques to provide a rigor-ous derivation of the Darcy scale model for precipitationand dissolution in porous media. The starting point is thepore scale model which is a coupled system of evolutionequations involving a parabolic equation. This models iontransport in the fluid phase of a periodic porous mediumand is coupled to an ordinary differential equations mod-eling dissolution and precipitation at the grains boundary(van Duijn and Pop (2004)). The main challenge is indealing with the dissolution and precipitation rates, whichinvolve a monotone but multi-valued mapping. In orderto pass to the limit in these rate functions at the bound-ary of the grains, we prove strong two scale convergencefor the concentrations at the microscopic boundary anduse refined arguments in order to identify the form of themacroscopic dissolution rate, which is again a multi-valuedfunction. The resulting upscaled model is consistent withthe Darcy scale model formally proposed in van Duijn, Kn-abner, Hengst (1995).
Kundan KumarUniversity of Texas, [email protected]
Maria Neuss-RaduUniversity of Erlangen-NurembergMathematics [email protected]
Sorin PopCASAEindhoven University of Technology
MS60
Quasi-stationary Approximation and Shadow Limitfor Reaction-diffusion-ode Models of BiologicalPattern Formation using Renormalisation GroupMethod
The talk is devoted to reduction of multiscale reaction-diffusion-ode models. Such systems of equations arise, forexample, from modeling of interactions between diffusingsignaling factors and processes localized in cells and on cellmembranes. We propose a rigorous approach based on therenormalisation group (RG) approximation of singularlyperturbed equations. We consider various scalings whichlead to quasi-stationary approximation or shadow limits.Applicability of the reduced models to study dynamics ofpattern formation is discussed on several examples frommathematical biology.
Anna Marciniak-CzochraUniversity of [email protected]
MS60
Upscaling of Interaction of Flow, Chemical Reac-tions and Deformation in Heterogenous Media
Experimental research on deformable porous media, likeliving tissues, is providing more and more detailed infor-mation on the nano- and micro-scale and this talk we willpresent mathematical modeling of reactive flow and trans-port and its interaction transport through tissue undervarying mechanical and chemical conditions. Here we con-sider equations on the fine scale modeling the real processesoccurring in the deformable pore space, in the solid struc-ture and in the interfaces (membranes). We are including
1. Fluid flow and diffusion, transport and reactions ofthe substances it transports.
2. Exchange of fluid and substances at the interfaces.Small deformation of the solid structure.
3. Changes of the structures and their mechanical prop-erties with the flow and with the substances concen-trations.
Our goal is to obtain the upscaled system modeling re-active flow through biological tissues on the macroscopicscale, starting from a system on the pore level. Using mul-tiscale techniques, we preform the scale limit and derivea macroscopic (effective) model system, preserving rele-vant information on the processes on the microscopic level.One obtains in the limit a system similar to the quasi-static Biot-law but coupled with chemical reactions. Usingthe characteristic time scalings resulting from the analy-sis of the real data, we will undertake further analysis andshow how the mechanics could be decoupled from the re-active flows. The modeling novelty in our paper is depen-dence of the Young modules, of the elastic structure, onthe concentration. Consequently, the reactive flows causesthe deformation. Adding diffusion, transport and reactionsof chemical substances and their interaction to mechanicsleads to new mathematical difficulties requiring new ideasand methods. In addition to the formal upscaling, we willgive some hints about the rigorous homogenization result.
Andro MikelicInstitut Camille Jordan, Departement de Mathematiques
CT15 Abstracts 123
Universite Lyon [email protected]
MS60
Capturing Secondary Nucleation Effects in Becker-Doering Interactions: The Homogenization Route
We present a continuum PDE-ODE model for collagen self-assembly describing the interplay between the change inthe polymer distribution and the evolution of monomers.We endow the model with periodic coefficients, where thesmall parameter is interpreted in this context as the ratioof lengths of monomers and fibrils. After applying a fixed-point homogenization argument and proving corrector es-timates, we use the microscopic information incorporatedin the first-order correctors to explain the so-called tur-bidity measurement. Finally, we compare qualitatively ourmultiscale modelling, mathematical analysis, and simula-tion results with experimental data. This work is a jointcollaboration with B. van Lith and C. Storm (Eindhoven).See [B.S. van Lith, A. Muntean, A. Muntean: A continuummodel for hierarchical fibril assembly. Europhysics Letters(EPL), 106 (2014), 08004.¡http://iopscience.iop.org/0295-5075/106/6/68004] and [O. Krehel, T. Aiki, A. Muntean:A thermo-diffusion system with Smoluchowski interactions:well-posedness and homogenisation. Networks and Hetero-geneous Media 9(2014), 4, 739-762] for further reading.
Adrian MunteanDepartment of Mathematics and Computer ScienceTU [email protected]
MS61
Multiobjective Optimal Control Techniques in En-ergy Management
We present a numerical set-oriented technique for the solu-tion of multiobjective optimal control problems. First, theproblem is transformed into a classical nonlinear multiob-jective optimization problem by an appropriate discretiza-tion of the control. Then, the entire Pareto set is computedusing both global subdivision and continuation methods.The functionality of the different algorithms is comparedand illustrated by the optimization of energy consumptionand temporal performance of an electric drive.
Michael DellnitzUniversity of [email protected]
Julian EcksteinHella KGaA Hueck & [email protected]
Kathrin FlasskampUniversity of [email protected]
Patrick FriedelHella KGaA Hueck & [email protected]
Christian HorenkampChair of Applied MathematicsUniversity of [email protected]
Ulrich KoehlerHella KGaA Hueck & [email protected]
Sina Ober-Bloebaum, Sebastian PeitzUniversity of [email protected],[email protected]
Sebastian TiemeyerHella KGaA Hueck & [email protected]
MS61
Integrated Building Energy Management: CurrentState and Key Technology Challenges
This presentation will outline the current key research anddemonstration activities of UTRC in the area of buildingenergy management including two main demonstration ef-forts on buildings and HVAC modelling and control cur-rently undertaken in the US and Ireland. The presentationwill highlight the key challenges and research opportunitiesfor the applied mathematics community that will drive themini-symposium discussion.
Konstantinos KouramasUnited Technologies Research Center [email protected]
Draguna VrabieUnited Technologies Research [email protected]
Marcin Cychowski, Stevo MijanovicUnited Technologies Research Center [email protected], [email protected]
MS61
Scheduling of Multi Energy Systems: Do We Re-ally Need a Global Optimum?
The definition of the optimal scheduling of a multi-energysystem is in general a very complex and computational in-tensive process. On the other hand, models and inputsto the optimization are affected by significant uncertainty.Starting from these considerations, the paper analyses therole of optimality versus the role of flexibility and robust-ness of the solution. Theoretical considerations are com-bined with real life experience in the optimization of dif-ferent real city quarters.
Antonello MontiE.ON Energy Research Center - RWTH [email protected]
Dirk Mueller, Rita StreblowRWTH Aachen [email protected], [email protected]
MS61
Fault Tolerant Control of Hvac Systems for EnergyEfficient Buildings
System-level or operational faults in building Heating Ven-
124 CT15 Abstracts
tilation and Air Conditioning (HVAC) systems, can havesignificant impact on the desired and expected building en-ergy performance and user comfort. Fault-tolerant controlsystems is characterized by its capability, after fault occur-rence, to recover performance close to the nominal desiredperformance. In this paper a method for fault decouplingin dynamic systems is presented. In an integrated design,the proposed approach is composed of two stages : Thefirst step is the detection and isolation of the fault basedon the generation of directional residuals while the secondstep is represented by the reconfiguration mechanism whichconsists in the estimation of new control parameters afterevaluation of the performance degradation.
Dominique SauterResearch Center for Automatic Contro, University [email protected]
MS62
Pontryagin Principles for Systems Governed byFunctional Differential Equations
We present a new proof of Pontryagin principle for finiteand infinite horizon nonlinear problems which are governedby a functional differential equation.
Joel BlotUniversity Paris [email protected]
MS62
Infinite-Horizon Multiobjective Optimal ControlProblems for Bounded Processes
Infinite-horizon multiobjective optimal control problemsfor bounded processes are studied in the discrete time case.These problems are governed by difference equations or in-equations. The results generalize to the multiobjective caseresults obtained for singleobjective optimal control prob-lems in that framework. Necessary conditions and suffi-cient conditions of Pareto optimality are provided namelyPontryagin maximum principles in the strong form and inthe weak form.
Naila HayekLaboratoire ERMES, University Pantheon Assas Paris 2.12 place du Pantheon. 75005 [email protected]
MS62
On the Convexity of the Value Function for A Classof Nonconvex Variational Problems: Existence andOptimality Conditions
We study a class of perturbed constrained nonconvexvariational problems depending on either time/state ortime/state’s derivative variables. Its (optimal) value func-tion is proved to be convex and then several related prop-erties are obtained. Existence, strong duality results andnecessary/sufficient optimality conditions are established.Moreover, via a necessary optimality condition in terms ofMordukhovich’s normal cone, it is shown that local minimaare global. Such results are given in terms of the Hamil-tonian function. Finally various examples are exhibitedshowing the wide applicability of our main results. This ajoint work with F. Flores-Bazan and G. Mastroeni.
Abderrahim Jourani
MS62
Periodicity in Infinite Horizon Problems of Opti-mal Harvesting
We investigate if the optimal harvesting of single specieson the infinite horizon can be proper periodic (a questionintensively discussed among practitioners). Two alterna-tive optimality concepts are used for a given objective in-tegrand: average revenue and discounted total revenue. Weshow that proper (asymptotically) periodic optimal solu-tions may appear if the heterogeneity of the species withrespect to age is taken into account. The analysis involvesa ”properness test” for the averaged problem and estab-lished relations between the two problems.
Vladimir M. Veliov, Anton BelyakovVienna University of [email protected], [email protected]
MS62
Structure of Extremals of Variational Problems inthe Regions Close to the Endpoints
We study the structure of approximate solutions of au-tonomous variational problems on large finite intervals. Inour research which was summarized in Zaslavski, Turnpikeproperties in the calculus of variations and optimal control,Springer, New York, 2006 we showed that approximate so-lutions are determined mainly by the integrand, and areessentially independent of the choice of time interval anddata, except in regions close to the endpoints of the timeinterval. In the present talk we study the structure of ap-proximate solutions in regions close to the endpoints of thetime intervals.
Alexander ZaslavskiThe Technion Israel Institute of [email protected]
MS63
An Approximate Controllability Result with Con-tinuous Spectrum: the Morse Potential with Dipo-lar Interaction
This note presents a positive approximate controllabilityresult for a bilinear quantum system modelling a chemicalbond. The main difficulties are due to the presence of acontinuous spectrum part for the uncontrolled Hamiltonian(modelled by a Morse potential) and the unboundedness ofthe interaction potential (dipolar interaction). Our proofuses averaging theory and spectral analysis.
Nabile BoussaidDepartment de MathematiquesUniversite de Franche [email protected]
Marco CaponigroCNAM, [email protected]
Thomas ChambrionInstitut Elie CartanUniversite de Lorraine
CT15 Abstracts 125
MS63
Inverse Problems in Quantum Control in Presenceof Uncertainties and Perturbations
The inversion problem of recovering the Hamiltonian anddipole moment is considered in a quantum control frame-work. The inversion process uses as inputs some measur-able quantities (observables) for each admissible control;however the implementation of the control is noisy (theperturbations are additive constants in a countable set ofvalues) and therefore the data available is only in the formof the law of the measured observable. Nevertheless it isproved that the inversion process still has unique solutions(up to some phase factors). Numerical illustrations sup-port the theoretical results.
Ying FuUniversite Paris [email protected]
MS63
Controllability of the Schrodinger Equation withThree Inputs Via Adiabatic Techniques
In this talk we will present a constructive method to con-trol the bilinear Schrodinger equation by means of threecontrolled external fields. This method can be used for in-stance to control the electromagnetic Schrodinger equationwith three controlled (electromagnetic) potentials. Themethod is based on adiabatic techniques and works if thespectrum of the Hamiltonian admits eigenvalue intersec-tions, with respect to variations of the controls, and if thelatter are conical.
Paolo [email protected]
Francesca ChittaroLSIS, Universite de [email protected]
MS63
Ensemble Controllability: Recent Results and Ap-plications to Quantum Inversion
The controllability of bilinear systems in presence of per-turbations is discussed. We give first some recent resultsconcerning the ensemble controllability of collection of bi-linear systems on connected, compact, simple Lie groups.The theoretical results are then applied to the controlla-bility of collection of perturbed systems with perturba-tions being constant on at least on some common inter-val. The circumstance of more general perturbations (time-dependent stochastic random processes) is also discussed.
Gabriel M. TuriniciCEREMADE Universite Paris [email protected]
MS64
Risk-Averse Control of Continuous-Time MarkovChains
We consider continuous time Markov process and designtime-consistent risk measurement. The construction is
based on discrete-time time-consistent Markov measuresand their dual representation. A general constructions aswell as several particular cases will be discussed.
Darinka DentchevaDepartment of Mathematical SciencesStevens Institute of [email protected]
MS64
On Stationary Markov Perfect Equilibrium in aRisk-Sensitive Dynamic Stochastic Decision Model
A stochastic dynamic choice model with the quasi-hyperbolic discounting is analysed. WIthin such a frame-work agents preferences may hinge on time. This require-ment, in turn, leads to a non-cooperative infinite horizonstochastic game played by a countably many selves repre-senting him during the play. A novel feature in our ap-proach is an application of the entropic risk measure tocalculating agent’s utility. As a result, we provide theo-rems on the existence of Markov perfect equilibria.
Anna JaskiewiczInstitute of Mathematics and Computer ScienceWroclaw University of [email protected]
Andrzej NowakUniversity of Zielona [email protected]
MS64
Risk-Averse Control of Discrete-Time Markov Sys-tems
We shall discuss fundamental questions of modeling risk indynamical systems and discuss the property of time consis-tency and the resulting interchangeability in optimal con-trol models. Special attention will be paid to discrete-timeMarkov systems. We shall refine the concept of time consis-tency of risk measures for such systems, introducing condi-tional stochastic time consistency. We shall also introducethe concept of Markov risk measures and derive their struc-ture. This will allow to derive a risk-averse counterpart ofthe dynamic programming equation. Finally, we shall re-view solution methods and present some examples.
Andrzej RuszczynskiRutgers [email protected]
MS64
A Risk-Averse Analog of the Hamilton-Jacobi-Bellman Equation
We introduce the concept of continuous-times risk measurefor diffusion process. The risk-averse control problem is es-tablished via FBSDE (forward-backward stochastic differ-ential equation) system. We derive the dynamic program-ming principle and prove the value function is a viscositysolution of the risk-averse Hamilton-Jacobi-Bellman equa-tion. We also discuss the approximation scheme when theclassical solution exists.
Andrzej RuszczynskiRutgers [email protected]
126 CT15 Abstracts
Jianing YaoOperations Research ProgramRutgers [email protected]
MS65
Data-Driven Modeling and Control of ComplexSystems: Sparse Sensing and Machine Learning
Abstract not available.
Steven BruntonUniversity of [email protected]
MS65
Self-Tuning Electromagnetic Systems
Abstract not available.
J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]
MS65
On Discovering Coherent Spatial-Temporal Modesfrom State and Control Input Histories with Spe-cial Emphasis on Infectious Disease Systems
Abstract not available.
Joshua L. ProctorInstitute for Disease [email protected]
MS65
Enhancing Data-Driven Koopman Spectral Analy-sis using Machine Learning Approaches
In recent years, Koopman spectral analysis has become apopular tool for the decomposition and study of nonlinearsystems. We will discuss methods that blend ideas frommachine learning with Koopman-based analyses includinga kernel reformulation of Extended Dynamic Mode De-composition (Extended DMD), which is a generalization ofDynamic Mode Decomposition. We will apply these tech-niques to both numerically generated data, where their ac-curacy can be quantified, and to experimentally obtaineddata from fluid dynamics.
Matthew O. WilliamsProgram in Applied and Computational MathematicsPrinceton [email protected]
Clarence RowleyPrinceton UniversityDepartment of Mechanical and Aerospace [email protected]
I. G. KevrekidisPrinceton [email protected]
MS66
Sliding Mode Control for Anti-Lock Braking Sys-
tems
The novel anti-lock brake algorithm is suggested. The al-gorithm is based on constrained extremum searching feed-back via the second order sliding mode. The algorithm al-lows to combine anti-lock brake system or traction systemwith yaw antiskid control. Convergence and stability of theclosed loop is proved via multimodal Lyapunov function.The yaw control algorithm developed gives additional mar-gins of vehicle stability during adverse driving maneuversover a variety of road conditions.
Sergey DrakunovDepartment of Physical SciencesEmbry-Riddle Aeronautical University, Daytona Beach,FL [email protected]
MS66
Yakubovich’s Oscillations in Systems with Discon-tinuous Nonlinearities
Sufficient conditions of attracting limit cycle existence fora linear system with sign nonlinearity are discussed. Itis assumed that the linear part of the system is stabiliz-able by an output feedback, the nonlinearity has linearnegative term plus positive one proportional to the out-put sign. Conditions of oscillation existence in the sense ofYakubovich for this class of systems are also presented.
Denis EfimovINRIA Lille-Nord59650 Villeneuve d’Ascq - [email protected]
Andrey PolyakovINRIA Lille-Nord59650 Villeneuve d’Ascq [email protected]
Wilfrid PerruquettiEcole Centrale de Lille, INRIA Lille Nord [email protected]
MS66
A Bifurcation Approach to Locate Stable Limit Cy-cles in Nonlinear Switched Systems and Its Appli-cation to Anti-Lock Braking Systems
If a switched system switches between nonlinear systems,then deriving effective criteria for the existence and stabil-ity of limit cycles is a difficult problem. Due to compli-cate friction characteristics the anti-lock braking systems(ABS) are essentially nonlinear. In this talk I propose anew approach where the limit cycle of a switched system(akin the ABS) is obtained as a bifurcation from a switchedequilibrium when a suitably designed parameter crosses thebifurcation value.
Oleg MakarenkovUniversity of Texas at [email protected]
MS66
Hybrid Anti-Lock Braking System Algorithms andSwitched Extended Braking Stiffness Observers:
CT15 Abstracts 127
Two Tools for Modern Braking Systems
We consider a class of anti-lock brake algorithms basedon wheel-deceleration thresholds, for which we analyze thestability of limit cycles using the Poincar map. We alsoconsider the observation of an unmeasured variable calledXBS. We propose an observer design based on Burckhardt’stire model. The observer’s convergence is analyzed usingtools for switched linear systems. Both experiments andsimulations confirm the convergence properties predictedby our theoretical analysis.
William Pasillas-LepineCNRS Ecole Superieure d’Electricite SUPELEC - UnivParis-Sud3 rue Joliot-Curie, 91192, Gif-sur-Yvette cedex, [email protected]
MS67
Control and Stabilization of Degenerate WaveEquations
The control of degenerate PDE’s arise in many applicationssuch as cloaking (building of devices that lead to invisibil-ity properties from observation), climatology, populationgenetics, and vision. For such equations, the diffusion op-erator degenerates on some subset of the spatial domain.We shall present some recent results on observability, con-trol and stabilization of degenerate wave equations. Thisis a joint work with Piermarco Cannarsa (University diRoma Tor Vergata, Italy) and Gunter Leugering (Friedrich-Alexander-Universitat Erlangen-Nurnberg, Erlangen, Ger-many).
Fatiha AlabauUniversite de Lorraine, [email protected]
MS67
Optimal Control on Reducing Carbon Emission
Abstract not available.
Jin LiangTongji UniversityShanghai, ChinaLiang [email protected]
MS67
Title Not Available - Souplet
Abstract not available.
Philippe SoupletLAGA, Institut Galilee, Universite Paris [email protected]
MS67
On An Optimal Control Problem Arising from In-duction Heating
Abstract not available.
Hong-Ming YinWashington State University
PP1
Outer Synchronization of Networks with MobileRobots
In this work, outer synchronization of coupled networkswith non-identical topology is reported. In particular,outer synchronization in nearest-neighbor and small-worldnetworks with coupled mobile robots is achieved by usingcomplex systems theory. By means of extensive numeri-cal simulations we show the advantages in outer synchro-nization of small-world networks against nearest-neighbornetworks. Different cases of interest are studied for a largenumber of mobile robots as nodes, including network syn-chronization without master mobile robot, and synchro-nization of networks with different master-slave configura-tions.
Adrian Arellano-DelgadoElectronics and Telecommunications Department,Scientific Research and Advanced Studies of [email protected]
Cesar Cruz-HernandezElectronics and Telecommunications Department,ScientificResearch and Advanced Studies of [email protected]
Rosa Martha Lopez-GutierrezFaculty of Engineering Architecture and Design,Baja California Autonomous [email protected]
PP1
A Novel Equation Error for Direct Adaptive Con-trol for a Class of First Order Systems with Exter-nal Disturbances
A novel equation error for direct adaptive control for a classof first order systems, is studied in this paper. It is shownthat the Output Error, Equation Error and the proposedequation error have different convergence speeds, transientresponse characteristics and the system robustness. Simu-lation results are used to show that the proposed equationerror is very much powered in disturbance rejection andhas less transient time oscillations.
Yaghoub AziziDepartment of Electrical EngineeringShahid Beheshti [email protected]
Alireza YazdizadehDepartment of Electrical EngineeringShahid Abbaspour [email protected]
PP1
Fractional Order Pid Controller Design for Mecha-tronic Systems
In this paper is described the general framework of frac-tional order PID controller parameter tuning. The methodis exemplified for two typical, basic models from mecha-tronic: the mass-spring-damper system and a benchmarksystem consisting of a DC motor, a gearbox, an elastic
128 CT15 Abstracts
shaft and a load. The simulation results highlight the ad-vantages of the method.
Roxana BothTechnical University of [email protected]
Dulf Eva, Muresan CristinaTechnical University of Cluj [email protected], [email protected]
PP1
Synchronization of Mobile Robots in DeterministicSmall-World Networks
This work presents the network synchronization of cou-pled mobile robots in deterministic small-world networks.Small-world networks are ubiquitous in real-life systems.Most previous models of small-world networks are stochas-tic. It is known to us all, stochasticity is a common featureof complex network models that generate small-world andscale-free topologies. In particular, we consider determinis-tic small-world networks created by edge iterations, i.e. thenetworks are growing due to deterministic algorithm. Thenetwork synchronization is achieved by using complex sys-tems theory, in which, for all reported case studies, we ob-tain synchronization of deterministic small-word networksby using the same coupling strength. That is, the increaseof mobile robots in the deterministic networks does notaffect the synchronization condition.
Rosa Martha Lopez-GutierrezUniversidad Autonoma de Baja [email protected]
Rigoberto Martınez-Clark, Daniel Reyes-De La Cruz,Cesar [email protected], [email protected],[email protected]
PP1
Clustering Methods for Control-Relevant Decom-position of Complex Process Networks
Complex process networks are ubiquitous in chemi-cal/energy plants, and typically cannot be controlled ef-fectively via purely decentralized control approaches. Weconsider the identification of constituent sub-networks suchthat the components of each network are strongly con-nected whereas different sub-networks are weakly con-nected. We propose a hierarchical clustering method togenerate manipulated input/controlled output clusters ofvarying modularity, using relative degree information todefine appropriate notions of distance (closeness) betweensuch clusters and compactness within clusters.
Prodromos DaoutidisUniversity of MinnesotaDept. of Chemical Engineering and Materials [email protected]
PP1
Observer Design for Distributed Parameter Sys-tems
In this paper we suggest a novel design of a nonlinear ob-server for distributed parameter system described by com-
bination of partial differential equations and ordinary dif-ferential equations. The proposed observer is based on slid-ing mode that provides robustness to possible mismatchesbetween the system model and the actual system. A for-mula for the observer gain is derived that guarantees sta-bility and convergence of the distributed observer state tothe actual system state. Several examples are consideredthat illustrate the approach.
Niloofar N. KamranEmbry-Riddle Aeronautical [email protected]
Sergey DrakunovDepartment of Physical SciencesEmbry-Riddle Aeronautical University, Daytona Beach,FL [email protected]
PP1
A Novel Tuning Method for Fractional Order PidController
The idea of the magnitude optimum method is to find acontroller that makes the frequency response from refer-ence to plant output as close as possible to unity for lowfrequencies. However, the method is not frequently usedin practice being sensitive to modeling errors. A novelapproach is proposed in this work, using fractional ordercontrollers, recognized for their robustness to plant gainvariations. The case study is the pilot plant of 13C sepa-ration.
Eva H. Dulf, Cristina Muresan, Roxana BothTechnical University of [email protected], [email protected], [email protected]
PP1
On Dynamics of Current-Induced Static Wall Pro-files in Ferromagnetic Nanowires Governed by theRashba Field
This article deals with the analytical study of propagationof static wall profiles in ferromagnetic nanowires under theeffect of spin orbit Rashba field. We consider the govern-ing dynamics as an extended version of Landau-Lifshitz-Gilbert equation of micromagnetism which comprise thenonlinear dissipation factors like dry-friction and viscous.We establish threshold and Walker-type breakdown esti-mates for the external sources in the steady regime andalso illustrate the obtained results numerically.
Sharad Dwivedi, Shruti DubeyIndian Institute of Technology [email protected], [email protected]
PP1
Construction of Hybrid Decision Processes
In the real world, we often encounter the complex phe-nomena which could not be analyzed only by probabilitytheory. In order to overcome this difficulty, Li and Liuhave proposed chance theory. In this paper we consider amethod of constructing of a Markov-type hybrid processfrom stochastic kernel and credibilistic kernel and give theexistence and the property of optimal policies.
Masayuki Kageyama
CT15 Abstracts 129
Nagoya City [email protected]
PP1
Title Not Provided - Kasimova
Randomly generated control of insects motion experimen-tally studied in formicarium and by mathematical modelof ants foraging paths from nest to food locus [1]. Pathsare impeded by barriers , viz. segments of given size, ran-domly centered-oriented with respect to nest-food straightline. When insects collide with the obstacle the trajectorybifurcates and the branch making an acute angle with thesmell gradient is selected. Trajectories consists of 1 or 3components. Space-realizations average travel time is eval-uated.
Rouzalia KasimovaGerman University of Technology in [email protected]
Denis TishinKazan Federal University, [email protected]
Yurii ObnosovKazan Federal University, RussiaInstitute of Mathematics and [email protected]
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Model-Free Optimal Tracking Control Via NuclearNorm Minimization
Model-based control is a two step procedure: 1) a modelof the plant is identified from data, 2) a controller is syn-thesized using the model. Model-free control aims to findthe control signal directly from the data. We show thatmodel-free control is equivalent to Hankel structured low-rank matrix approximation and completion. The missingdata in the matrix formulation is the to-be-found controlsignal and the approximation is the tracking error. Nu-clear norm relaxation is used for numerical solution of theproblem.
Ivan Markovsky
Vrije Universiteit Brussel (VUB)[email protected]
PP1
Extension of the Sethi Model to the Advertising ofDigital Products
In this paper, a model is formulated that modifies the Sethimodel of advertising optimization to incorporate uniquefeatures present in the mobile game space. Although theoptimization of advertising in traditional industries hasbeen thoroughly studied, the optimization models used lacksufficient predictive power for several emerging market sec-tors. For the free-to-play video game industry in particular,there are issues that arise in the form of uncertain revenuefrom users and the effect of the ranking systems used forthese games. This paper compares the modified and origi-nal Sethi models and it is shown how little or no advertisingin the video game industry can still result in a large marketshare given sufficient virality parameters for the game.
Alex D. Murray, Allan MacIsaac
University of Western [email protected], [email protected]
PP1
Feedback Stabilization of a Fluid-Structure Model:Theory and Numerics.
We study the stabilization of the Navier-Stokes equationsin 2D around an unstable stationary solution. The config-uration corresponds to a flow around a bluff body. Twobeams are located at the boundary of the body and theirdeformations are used to stabilize the flow. The controlis a force in the beam equations. We study theoreticallyand numerically the feedback stabilization of this systemcoupling the Navier-Stokes equations with the beam equa-tions.
Moctar Ndiaye, Michel FournieInstitut de Mathematiques de [email protected],[email protected]
Jean-Pierre RaymondUniversite’ Paul Sabatier, [email protected]
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Robustified H2-Control of a System with LargeState Dimension
We consider the design of an output feedback controllerfor a large scale system like the linearized Navier-Stokesequation. We design an observer-based controller for a re-duced system that achieves a compromise between concur-ring performance and robustness specifications. This con-troller is then pulled back to the large scale system suchthat closed-loop stability is preserved, and such that thetrade-off between the H2- and H∞-criteria achieved in re-duced space is preserved. The procedure is tested on asimulated fluid flow study.
Laleh RavanbodInstitut de Mathematiques de Toulouse, [email protected]
Dominikus NollUniversite Paul SabatierInstitut de [email protected]
Jean-Pierre RaymondUniversite’ Paul Sabatier, [email protected]
Jean-Marie BuchotInstitut de Mathematiques de Toulouse, [email protected]
PP1
Design of a Soft Sensor Based on Neural Networksfor the Estimation of High Differential Pressure onHigh Temperature Shift Catalyst in Ammonia Pro-duction Plants
The ammonia production plants use to experience an incre-ment of the differential pressure across the High Temper-ature Shift (HTS) catalyst. This issue results in reduced
130 CT15 Abstracts
ammonia production due to a continuous plant rate reduc-tion to accommodate the increasing pressure and also asolid waste formation. An alternative method for monitor-ing the pressure is a soft sensor based on in neural networks.In the present work, a neural network has been design andtraining relating the pressure (output) with a set of theprocess variables and kinetic of the reaction. The resultsindicated an accuracy of 4%. A soft control system basedon the neural network has been found to substantially goodfor the reduction of pressure fluctuations. This kind of sys-tem can be used to prevent the same problem in any othersimilar ammonia plants.
Carmen Riverolchemical [email protected]
Vashti GoorahlalChemical Engineering DepartmentUniversity of the West [email protected]
PP1
Bioeconomic Analysis Supports the EndangeredSpecies Act
The Endangered Species Act (ESA) was enacted to re-store declining natural populations. The ESA mandatesspecies protection irrespective of costs; this translates torestriction of activities harming endangered populations.We discuss criticisms of the ESA in the context of publicland management and examine under what circumstancebanning non-conservation activity on multi-use lands canbe socially optimal. We develop a bioeconomic modelto frame the management problem and identify scenarioswhere ESA-imposed regulation is optimal.
Kehinde R. SalauThe University of [email protected]
Eli FenichelYale [email protected]
PP1
Optimal Identification of Distributed System
We seek to find effective identification algorithms for a sys-tem that involves a set of spatially distributed sensors anda fusion center. The sensors make local observations whichare noisy versions of a signal of interest. Each sensor trans-mits compressed information about its measurements tothe fusion center which should recover the original signalwithin a prescribed accuracy. The key problem is to iden-tify models of the sensors and the fusion center. We showhow the required models follow from the solution of theassociated least squares problems.
Anatoli TorokhtiUniversity of South AustraliaSchool of Information Technology & [email protected]
PP1
Controller Design for High Precision Servo Sys-tems with Model Uncertainties, Saturations and
Disturbances
This paper proposes a novel adaptive backstepping slid-ing mode control methodology for an X-Y high precisionservo manipulation system. The control methodology isproposed for tracking desired motion trajectories in thepresence of unknown system parameters, input saturations,and external disturbances. In this study, an auxiliarystructure is employed to analyze the effect of input sat-urations, by which the proposed control scheme is success-fully designed to achieve a high tracking performance in thepresence of the aforementioned conditions. The stability ofthe closed-loop system is analyzed and the proposed con-trol architecture is tested in real-time experiments. Finally,simulation results and experimental results are provided toillustrate the effectiveness of the proposed criteria.
Peng YanBeihang [email protected]
Yangming ZhangBeihang [email protected]
Zhen ZhangTsinghua [email protected]
