Editorial Mathematical Modeling, Analysis, and Control of Hybrid Dynamical Systemsdownloads.hindawi.com/journals/mpe/2013/820948.pdf · 2019-07-31 · Mathematical Modeling, Analysis,

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013, Article ID 820948, 3 pageshttp://dx.doi.org/10.1155/2013/820948

EditorialMathematical Modeling, Analysis, and Control ofHybrid Dynamical Systems

Peng Shi,1,2 Hamid Reza Karimi,3 Rongni Yang,4 and Xiaojie Su5

1 School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA 5005, Australia2 College of Engineering and Science, Victoria University, Melbourne, VIC 8001, Australia3 Department of Engineering, Faculty of Technology and Science, University of Agder, 4898 Grimstad, Norway4 School of Control Science and Engineering, Shandong University, Jinan 250061, China5 School of Automation, Chongqing University, Chongqing 400044, China

Correspondence should be addressed to Peng Shi; [email protected]

Received 19 November 2013; Accepted 19 November 2013

Copyright © 2013 Peng Shi et al.This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Most of the dynamical systems that we have around us maybe reasonably described in discrete time or continuous timeand deterministic case or stochastic case. However, a largeclass of such physical systems may be modelled as hybridones; that is, to the continuous state variable, a discreterandom variable, called as the mode, or regime, is appended.For instance, these may result from the abrupt phenomenasuch as component and interconnection failures, parame-ters shifting, tracking, and the time required to measuresome of the variables at different stages. Interactions ofthese continuous and discrete dynamics appear in responseto discrete, instantaneous events and in response to dynam-ics as described by differential or difference equations intime. Therefore, for hybrid dynamical systems (includingMarkovian jumping systems, variable-structure systems withdiscontinuous dynamical systems, and switching systems),there are many challenging issues, for example, mathematicalmodeling, stochastic analysis, hybrid control and observerdesign, optimal estimation and filtering, fault detection anddiagnosis, model reduction, and applications of hybrid sys-tems to complex and large-scale systems, that need to besolved.

In this special issue there are twenty-nine papers, ofwhich two are related to stability analysis and stabilization ofMarkovian jumpnonlinear systems and the nonlinear neutraldelay differential equations, and eleven solve the problemof controller design for complex dynamical systems. Four

articles discuss how to estimate the unmeasurable systemstates and design a filter by different approaches. There arealso two papers focusing on fault detection for non-Gaussianstochastic delayed systems and nonlinear impulsive switchedsystems. Another article deals with the parallel encryptionalgorithm of piecewise linear chaotic systems. Finally, eightpapers cover the problem of mathematical modeling andoptimal performance for dynamic systems, and one articlecovers the model approximation/reduction for Markovianjump systems with deficient mode information.

During the past decades, the problems of stability analysisand controller design have received significant attention forhybrid dynamical systems in engineering applications. “Full-state linearization and stabilization of SISO Markovian jumpnonlinear systems” by Z. Lin et al. concerns the linearizationand stabilizing control design problems for a class of SISOMarkovian jump nonlinear systems, and “Nonlinear stabilityand convergence of two-step Runge-Kutta methods for neutraldelay differential equations” by H. Yuan et al. is devotedto the stability and convergence analysis of the two-stepRunge-Kutta methods with the Lagrange interpolation ofthe numerical solution for a set of nonlinear neutral delaydifferential equations. “Dynamic output feedback passive con-trol of uncertain switched stochastic systems with time-varyingdelay” by H. Jia et al. and “Delay-dependent 𝐻

∞Control for

networked control systems with large delays” by Y. Wang et al.are concerned with issues of controller design for uncertain

2 Mathematical Problems in Engineering

switched stochastic delayed systems and networked controlsystems with large delays, respectively. Moreover, “Observer-based decentralized control for uncertain interconnected sys-tems of neutral type” by H. Hu et al. solves the observer-based decentralized control problem for a class of uncer-tain interconnected systems of neutral type, and “Observer-based robust control of uncertain switched fuzzy systems withcombined switching controller” by H. Yang et al. proposes anobserver-based robust controller design method for a classof switched fuzzy time-delay systems involving uncertaintiesand external disturbances. “Reliable control for time-varyingdelay switched fuzzy systems with faulty actuators based onobservers switching method” by L. Zhang and J. Wu deals withthe reliable control problem of nonlinear systems representedby switched fuzzy systems with time-varying delay. “Outputtracking control of switched hybrid systems: a Fliess functionalexpansion approach” by F. He et al. presents the solution ofthe output tracking problem for a class of nonlinear affinesystems. “Active tension control for WT wheelchair robot byusing a novel control Law for holonomic or nonholonomicsystems” by J. Wang et al. gives the novel active tensioncontrol law for holonomic or nonholonomic robotic systems.“A hybrid approach for coordinated formation control ofmultiple surface vessels” by M. Fu and J. Jiao investigates thecoordination control of multiple marine vessels in differentoperational modes, and “Horizontal and vertical rule basesmethod in fuzzy controllers” by S. Aminifar and A. binMarzuki describes a new method of uncertainty descriptionin fuzzy controllers by introducing the concept of horizontaland vertical rule bases in fuzzy controllers and their rolls inthe ease of extracting the optimum control surface by usinglesser rules than traditional fuzzy systems. “Controllabilityof continuous bimodal linear systems” by J. Ferrer et al.considers bimodal linear systems consisting of two lineardynamics acting on each side of a given hyperplane, assumingcontinuity along the separating hyperplane, while “Upperbounds for the distance between a controllable switched linearsystem and the set of uncontrollable ones” by J. Clotet and M.D. Margret obtains an upper bound for the distance from acontrollable switched linear system to a set of uncontrollableones.

On the other hand, the state estimation and filter prob-lems of dynamical hybrid systems have been investigatedextensively, since they are very useful in signal processing andengineering applications. “An FEM-based state estimationapproach to nonlinear hybrid positioning systems” by Y.-X.Zhao et al. proposes a finite element method based stateestimation approach to hybrid positioning systems. “𝐻

∞

channel estimation for DS-CDMA systems: a partial differenceequation approach” by W. Wang and C. Han gives a numberof different algorithms for channel estimation problems withthe statistics of the channel noise and observation noiseexactly known. “IMM iterated extended 𝐻

∞particle filter

algorithm” by Y. Wan et al. puts forward one interactingmultiple model iterated extended 𝐻

∞particle filter algo-

rithm to solve the tracking problem of radar maneuveringtarget in nonlinear system model and non-Gaussian noisebackground. “Missing value estimation for microarray databy Bayesian principal component analysis and iterative local

least squares” by F. Shi et al. proposes a BPCA-iLLS method,which is an integration of two commonly used missingvalue estimation methods—Bayesian principal componentanalysis (BPCA) and local least squares (LLS). “Fault detec-tion for nonlinear impulsive switched systems” by J. Li etal. addresses a novel fault detection filter approach fornonlinear impulsive switched systems, while “Fault detectionfor non-Gaussian stochastic systems with time-varying delay”by T. Li et al. studies fault detection for non-Gaussianstochastic systems by constructing an augmented Lyapunovfunctional.

The problems of mathematical modeling and identifica-tion have long been the mainstream of research topics, andmuch effort has been made for hybrid dynamical systems.“Fuzzy logic-based aerodynamic modeling with continuousdifferentiability” by R. C. Chang presents a modeling methodbased on a fuzzy-logic algorithm to establish aerodynamicmodels by using the datasets from flight data recorders.“Modeling and robust trajectory tracking control for a novel six-rotor unmanned aerial vehicle” by C. Yang et al. investigatesmagical modeling and trajectory tracking control problemsfor a novel six-rotor unmanned aerial vehicle. “Greenhousemodeling using continuous timed Petri nets” by J. L. Tovanyet al. explores a continuous timed Petri nets (ContPN) basedgreenhouse modeling methodology which is based on thedefinition of elementaryContPNmodules.Moreover, “Vibra-tion isolation platform with multiple tuned mass dampers forreaction wheel on satellites” by Y. Zhang et al. proposes anovel vibration isolation system for reaction wheel, includinga multistrut vibration isolation platform and multiple tunedmass dampers. “Optimization of biodiesel injection parametersbased on support vectormachine” by F. Shi et al. establishes theeffective specific fuel consumption prediction model basedon support vector machine. “Gabor Weber local descriptor forbovine iris recognition” by S. Sun et al. identifies a novel localdescriptor, named Gabor Weber local descriptor for bovineiris recognition. “New approaches to identification of PWARXsystems” by Z. Lassoued and K. Abderrahim provides theclustering based procedures for the identification of discrete-time hybrid systems in the piecewise affine form. “Theresearch of mathematical method and position control of actu-ator in power switchgear” by E. Dong et al. does the researchof mathematical method and position control, which is basedon permanent magnetic actuator, and analyzes the discharg-ing and free-wheeling process. Also, for many high-orderhybrid dynamical systems, model approximation/reductionhas been a hot issue to be solved in recent years. “𝐻

∞model

reduction for discrete-time Markovian jump systems withdeficientmode information” byY.Wei et al. solves the problemof𝐻∞model reduction for a class of discrete-timeMarkovian

jump linear systems (MJLSs) with deficient mode infor-mation, which simultaneously involves the exactly known,partially unknown and uncertain transition probabilities. Onanother active research front, “Aparallel encryption algorithmbased on piecewise linear chaotic map” by X. Wang and D.Chen introduces a parallel chaos-based encryption algorithmfor taking advantage of multicore processors and designs theparallel algorithmwith amaster/slave communicationmodelwith the message passing interface.

Mathematical Problems in Engineering 3

It is noted that both optimal analysis and synthesis forcomplex hybrid dynamical systems have always been hotissues in the field of control theory for the recent decades.Recently, the concerned hybrid dynamical plants in net-worked control systems have been extensively investigateddue to their broad applications in engineering, in whichthe phenomena of data packet loss and networked-inducedcommunication time-delay have attracted more and moreresearch interest. As is well known, with increasingly large-scale and complicated industrial processes, there are externaldisturbances originating from various sources in almost allcontrolled systems. Thus, the research of robust control anddisturbance attenuation performance for complex hybriddynamical systems with time-delay and data packet loss isa challenging problem. On the other hand, state estima-tion/filter and model reduction for complex hybrid dynami-cal systems have also received considerable attention becauseof their applicability and significance in various areas. Insummary, almost all articles in this special issue concernthose recent foci and somenewdevelopmentswhich emergedin complex hybrid dynamical systems. Moreover, many prac-tical applications can also be found in this special issue, suchas holonomic or nonholonomic robotic systems, multiplesurface vessels, six-rotor unmanned aerial vehicle, and powerswitchgear.

Of course, the selected topics and papers are not acomprehensive representation of the area of this specialissue. Nonetheless, they represent the rich and many-facetedknowledge and we hope the readers will find them wellreadable and useful as much as we do.

Acknowledgments

Wewould like to express our great appreciation to the authorsfor their remarkable contributions in assisting us. Finally, allreviewers’ fundamental work on these papers is also verygreatly acknowledged.

Peng ShiHamid Reza Karimi

Rongni YangXiaojie Su

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Editorial Mathematical Modeling, Analysis, and Control of Hybrid Dynamical Systemsdownloads.hindawi.com/journals/mpe/2013/820948.pdf · 2019-07-31 · Mathematical Modeling, Analysis,