Editorial Nonlinear Analysis of Dynamical Complex Networks 2014downloads.hindawi.com/journals/aaa/2014/976231.pdf · 2019-07-31 · Editorial Nonlinear Analysis of Dynamical Complex

EditorialNonlinear Analysis of Dynamical Complex Networks 2014

Zidong Wang,1,2 Bo Shen,3 Hongli Dong,4,5 Jun Hu,5,6 Xiao He,7 and Derui Ding8

1 Department of Computer Science, Brunel University, Uxbridge, Middlesex UB8 3PH, UK2Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University,Jeddah 21589, Saudi Arabia

3 School of Information Science and Technology, Donghua University, Shanghai 200051, China4College of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China5 Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China6Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China7Department of Automation, Tsinghua University, Beijing 100084, China8Department of Applied Mathematics, Anhui Polytechnic University, Wuhu 241000, China

Correspondence should be addressed to Zidong Wang; [email protected]

Received 14 September 2014; Accepted 14 September 2014; Published 21 December 2014

Copyright © 2014 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We have solicited submissions from electrical engineers,control engineers, computer scientists, and mathematicians.After a rigorous peer review process, 28 papers have beenselected that provide overviews, solutions, or early promises,to manage, analyze, and interpret dynamical behavioursof complex systems. These papers have covered both thetheoretical and practical aspects of complex systems in thebroad areas of dynamical systems, mathematics, statistics,operational research, and engineering.

For networked control systems (NCSs), especially large-scale systems such as multiagent systems and systems oversensor networks, the complexities are inevitably enhanced interms of their degrees or intensities because of the usage of thecommunication networks. This special issue starts with twosurvey papers on the recent advances of performance analysiswith network-enhanced complexities and communicationprotocols for NCSs. In the paper entitled “Performanceanalysis with network-enhanced complexities: on fading mea-surements, event-triggered mechanisms, and cyber attacks”by D. Ding et al., the focus is to provide a timely reviewon the recent advances on the performance analysis andsynthesis with three sorts of fashionable network-enhancedcomplexities, namely, fading measurements, event-triggeredmechanisms, and attack behaviours of adversaries. Thesethree kinds of complexities are introduced in detail according

to their engineering backgrounds, dynamical characteristic,and modelling techniques. Accordingly, the developmentsof the performance analysis and synthesis issues for variousnetworked systems are systematically reviewed. Finally, somechallenges are illustrated by using a thorough literaturereview and some possible future research directions arepointed out. Subsequently, in the paper entitled “Time- andevent-driven communication process for networked control sys-tems: a survey” by L. Zou et al., a timely review on the recenttheoretical developments of various sampling procedures andcommunication protocols in time-driven communicationand event-driven communication for NCSs is given. Theresults discussed include, but are not limited to the followingaspects: (1) NCSs with time-driven sampling procedures,(2) NCSs with event-driven sampling procedures, and (3)NCSs subject to different communication protocols. Somerecent advances on the analysis and synthesis issues of NCSswith different sampling procedures (time- and event-drivensampling) and protocols (static and dynamic protocols)are provided. These sampling procedures and protocols arefirstly introduced in detail according to their engineeringbackgrounds as well as dynamic natures. Subsequently, therecent developments of the stabilization, control, and filteringproblems are systematically reviewed and discussed in greatdetail. Finally, future research challenges for analysis and

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014, Article ID 976231, 4 pageshttp://dx.doi.org/10.1155/2014/976231

2 Abstract and Applied Analysis

synthesis problems of NCSs with different communicationprocesses are proposed.

In the past decades, the stability analysis of the dynamicalcomplex networks has attracted much research attention. Inthe work entitled “Global 𝜇-stability of complex-valued neuralnetworks with unbounded time-varying delays” by X. Chenet al., the sufficient conditions are given to guarantee thedesirable stability when the time delays are unbounded. Byconstructing an appropriate Lyapunov-Krasovskii functionaland employing the free weighting matrix technique, somedelay-dependent criteria are provided to ensure the global𝜇-stability of the addressed complex-valued neural networksby using the linear matrix inequality (LMI) approach. Twoexamples are given to show the effectiveness and less con-servatism of the proposed criteria. The stability in meanof partial variables for coupled stochastic reaction-diffusionsystems on networks (CSRDSNs) is discussed in “Stabilityin mean of partial variables for coupled stochastic reaction-diffusion systems on networks: a graph approach” by Y.Kao and H. Karimi. By transforming the integral of thetrajectory with respect to spatial variables as the solution ofthe stochastic ordinary differential equations and using Itoformula, some novel stability criteria are proposed to ensurethe uniform stability in mean, asymptotic stability in mean,uniformly asymptotic stability in mean, and exponentialstability in mean of partial variables for CSRDSNs. Thesestability conditions have a close relation with the topologyproperty of the network. Also, a systematic method isestablished to construct the global Lyapunov function forCSRDSNs by using the graph theory. The Cohen-Grossberg-type BAMneural networksmodel has promising potential forthe tasks of parallel computation and associative memory. Inthe paper entitled “Exponential stability of periodic solutionsfor inertial type BAM Cohen-Grossberg neural networks” byC. Miao and Y. Ke, the existence and exponential stabilityof periodic solutions are studied for inertial type BAMCohen-Grossberg neural networks. By properly choosingvariable substitution, the system considered is transformedto first order differential equation. Then, by constructingsuitable Lyapunov functional and using differential meanvalue theorem, some sufficient conditions are provided toensure the existence and exponential stability of periodicsolutions for the system. Finally, two numerical examplesare used to demonstrate the effectiveness of the proposedresults. The stability with mode constraint is investigated in“Stability of infinite dimensional interconnected systems withimpulsive and stochastic disturbances” byX. Xu et al. for a classof infinite dimensional look-ahead interconnected systemswith impulsive and stochastic disturbances. A set of sufficientconditions is given to guarantee the stability with modeconstraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochasticdisturbances. It is shown that the obtained conditions haveless conservatism than the existing results. Secondly, by thesliding mode control method, the controller is designedfor a class of look-ahead vehicle following systems withuncertainties. Also, the domain of the control parameters ofthe systems is proposed. Finally, a numerical simulation isgiven to demonstrate the usefulness of the proposed results.

Recently, the synchronization of dynamics complex net-works has attracted a great deal of research interest. Inthe paper entitled “Nonlinear dynamic analysis and syn-chronization of four-dimensional Lorenz-Stenflo system andits circuit experimental implementation” by C.-H. Yang andC.-L. Wu, the adaptive generalized synchronization is dis-cussed for four-dimensional Lorenz-Stenflo system withuncertain chaotic parameters strategy. By electronic circuitimplementation of the proposed four-dimensional Lorenz-Stenflo system, it is shown that the chaotic attractors doexist physically. The problem of the impulsive projectivesynchronization is considered in “Projective synchronizationanalysis of drive-response coupled dynamical network withmultiple time-varying delays via impulsive control” by S.Zheng for a drive-response coupled dynamical networkwith dynamical nodes delay and both nondelayed couplingand multiple delayed couplings. Sufficient conditions aregiven to guarantee the projective synchronization by usingthe stability analysis of the impulsive functional differentialequation. An impulsive controller is also designed. Theproblem of exponential synchronization is investigated in“Exponential synchronization of two nonlinearly coupled com-plex networks with time-varying delayed dynamical nodes” byW. Shao for two nonlinearly coupled dynamical networkswith identical time-delayed dynamical nodes via adaptivecontrol. Based on the Lyapunov theory and by conduct-ing extensive mathematical analysis, some synchronizationcriteria are proposed. Numerical examples are provided toillustrate the usefulness of the developed synchronizationconditions. Further research attention can bemade to discussthe exponential synchronization problem for drive-responsenonlinearly coupled dynamical networkwith noise. Similarly,the cluster projective synchronization problem is discussed in“Cluster projective synchronization of fractional-order complexnetwork via pinning control” by L. Yang et al., for complexdynamical networks with fractional-order dynamical nodes.The pinning controllers are designed according to the nodesproperty. Some simple criteria are established for clustersynchronization for any initial values through an effectivecontrol scheme. In the paper entitled “Exponential outersynchronization between two uncertain nonlinearly coupledcomplex networks” by Y. Wu et al., the exponential outer syn-chronization and parameter identification are investigatedfor two uncertain time-varying complex dynamical networkswith nonlinear coupling, time delays, and different topolog-ical structures. Based on the Lyapunov stability theory, anadaptive control scheme is proposed to achieve exponentialouter synchronization between drive and response networks.A network model with a scale-free feature and clusterstructure is constructed in “Hub-induced synchronization inscale-free networks with cluster structure” by J. Zhang et al.Some sufficient conditions are proposed to achieve the clustersynchronization. It is shown that the cluster synchronizationcan be guaranteed by increasing the coupling strength ofthe cluster hubs. Moreover, in the paper entitled “Eigenvaluebased approach for global consensus inmultiagent systemswithnonlinear dynamics” by W. Qian and L. Wang, the problemof global consensus is discussed for nonlinear multiagentsystems with asymmetrically coupled identical agents.

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Over the past decades, the design of the controllers haslong been the mainstream of research topics and much efforthas beenmade for dynamical complex networks. In the paperentitled “Impulsive control and synchronization of complexLorenz systems” by S. Aly et al., the problems of impulsivecontrol and synchronization are studied for complex Lorenzsystems. The impulsive control technique is employed tosynchronize the chaotic attractors of the addressed complexLorenz systems. Some new criteria are provided to guaranteethe global exponential stability and asymptotical stability ofimpulsively controlled complex Lorenz systems. To improvethe tracking performance and to shorten the response time,an improved PID intelligent control algorithm is developedin “PSO-RBF neural network PID control algorithm of electricgas pressure regulator” by Y. Zhong et al. and then appliedto the electric gas pressure regulator. Theoretical analysisand experimental results demonstrate that the proposedalgorithm improves the control accuracy, response speed, andtracking performance of electric gas pressure regulator. In thework entitled “Nonlinear dynamic surface control of chaos inpermanent magnet synchronous motor based on the minimumweights of RBF neural network” by S. Luo, a new design of thenonlinear dynamic surface controller based on theminimumweights of RBF neural network is proposed for permanentmagnet synchronous motor with the unknown parame-ters, disturbances, and chaos. The RBF neural network isemployed to approximate unknown nonlinear functions andthe adaptive method is introduced to deal with the unknowncontrol gain in the system.The proposed controller can guar-antee the boundedness of all the signals in the closed-loopsystem and the tracking error converges to a small neighbour-hood of the origin. To guarantee the finite-time stability of theerror system between themaster system and the slave system,an active control method is proposed in “Finite-time synchro-nizing control for chaotic neural networks” by C. Zhang et al.for the slave system based on the terminal attractor. To realizethe desired controller, an effective state observer based on aspecial tracking differentiator is designed to estimate all theuncertainties and disturbances. The approximate finite-timestability of the closed-loop system is analyzed based on thesingular perturbation theory.Moreover, the developed resultsare applied to some chaotic neural networks. Numericalsimulations are employed to demonstrate the effectiveness ofthe proposed control strategy. In the paper entitled “Adaptivecontrol of nonlinear discrete-time systems by using OS-ELMneural networks” by X.-L. Li et al., by using online sequen-tial extreme learning machine (OS-ELM) neural networks,the identification and control are discussed for nonlineardynamic plants. The adaptive controller based on OS-ELMneural network model is constructed. A guaranteed-costobserver-based control problem is studied in “Observer-based robust control for spacecraft rendezvous with thrustsaturation” by N. Wan et al. for thrust-limited rendezvous innear-circular orbits. An optimal observer-based rendezvouscontroller with a less conservative saturation control lawis developed. Finally, in the work entitled “Discrete-timeevent-triggered control of nonlinear wireless networked control

systems” by S. Hu et al., the stabilization problem is investi-gated for nonlinear discrete-time NCSs with event-triggeringcommunication scheme with signal transmission delay.

As is well known, the analysis on the applications of thedynamical complex networks has important significance. Inthe paper entitled “The degree analysis of an inhomogeneousgrowing network with two types of vertices” by H. Huang, aninhomogeneous growing network with two types of verticesis discussed. The degree sequences of two different types ofvertices are investigated. It is shown that the asymptoticaldegree distribution of type for this process is power law andthe strong law of large numbers for degree sequences of twodifferent types of vertices is given. The dissipative propertyis considered in “On the global dissipative and multipeakondissipative behavior of the two-component Camassa-Holmsystem” by Y. Wang et al., for two-component Camassa-Holm system after wave breaking. The global dissipativesolutions of the two-component Camassa-Holm system andthe multipeakon dissipative solutions are obtained. In thework entitled “Observation of a class of disturbance in timeseries expansion for fractional order systems” by Y. Wei etal., the methods of observer for fractional order systems intime series expansion disturbance are discussed. Accordingto the maximum degree of disturbance polynomials, the dis-turbances are divided into three categories. New developedapproaches have greater design freedom and the designedobservers have a faster convergent speed. The behaviourpreferences of Wechat users in knowledge propagation aresummarized and a Wechat knowledge propagation model isintroduced in “Study on knowledge propagation in complexnetworks based on preferences, taking Wechat as example”by S. Chen and W. He. A knowledge propagation networkaccording to the individual characteristics and interactiverules is constructed. In the paper entitled “Algorithms forfinding inverse of two patterned matrices over 𝑍𝑝” by X. Jiangand K. Hong, two new patterned matrices are discussed.Accordingly, the basic properties are discussed. Two differentalgorithms are developed based on theNewton-Hensel liftingand Chinese remaindering. Moreover, the cost in terms of bitoperations for each algorithm is given. The European optionpricing problem with transaction costs is investigated for arisky asset price model with Levy jump in “European optionpricing with transaction costs in Levy jump environment” byJ. Li et al. By the aid of arbitrage pricing theory and thegeneralized Ito formula including Poisson jump, the explicitsolution to the risk asset price model is provided. Accordingto the arbitrage-free principle, the discrete-timemodel is firstobtained. Then, the transaction costs are introduced in eachsmall time interval. The explicit solutions of the Europeanoptions pricing formula with transaction costs are given forthe risky asset price model with Levy jump. In the work enti-tled “On skew circulant typematrices involving any continuousFibonacci numbers” by Z. Jiang et al., the invertibility of theskew circulant type matrices is discussed and the explicitdeterminants are given by constructing the transformationmatrices. In the paper entitled “Fault detection for wirelessnetworked control systems with stochastic switching topologyand time delay” by P. Guo et al., the fault detection problem isstudied for a class of discrete complexwirelessNCSs. By using

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the Lyapunovmethod and stochastic analysis techniques, suf-ficient conditions are given to guarantee the existence of thefilters satisfying the desired performance requirement.

Acknowledgments

This special issue is a timely reflection of the research progressin the area of nonlinear analysis of dynamical complexnetworks. We would like to acknowledge all authors for theirefforts in submitting high-quality papers. We are also verygrateful to the reviewers for their thorough and on timereviews of the papers.

Zidong WangBo Shen

Hongli DongJun HuXiao He

Derui Ding

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Editorial Nonlinear Analysis of Dynamical Complex Networks 2014downloads.hindawi.com/journals/aaa/2014/976231.pdf · 2019-07-31 · Editorial Nonlinear Analysis of Dynamical Complex