Hao Shen

Quanxin Zhu

Shuping He

Yanyan Yin

Zhengguang Wu

Abstract and Applied Analysis

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Robust Control, Optimization, and Applications to Markovian Jumping Systems

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EditorialRobust Control, Optimization, and Applications to MarkovianJumping SystemsShuping He,1 Zhengguang Wu,2 Hao Shen,3 Yanyan Yin,4 and Quanxin Zhu51 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China2National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University,Hangzhou 310058, China3 School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, China4Department of Mathematics and Statistics, Curtin University, Perth, WA 00301J, Australia5 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaCorrespondence should be addressed to Shuping He; shuping.he@ahu.edu.cnReceived 27 May 2014; Accepted 27 May 2014; Published 24 June 2014Copyright © 2014 Shuping He 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.Markovian jumping systems have arisen naturally in themathematical modeling of phenomena spanning disciplinesin the social sciences, natural sciences, and engineering. Thiskind of stochastic dynamical systems can be employed tomodel the dynamics when parameters are subject to randomabrupt changes due to sudden environment changes, subsys-tem switching, system noises, executor faults, and so forth.Much attention has been given to modeling, optimization,and real applications of such stochastic dynamical systemsin the literature in recent years. As the advanced controland optimization will provide a basis for the design andapplication of such stochastic systems, these advanced tech-niques would result in substantial and sustainable benefits.The accepted papers in this special issue include stochasticstability, stabilization, stochastic control optimization, systemmodeling and identification methods, predictive control,signal processing, robust filtering, multiagent systems, net-worked control systems, time-delayed systems, neural net-works, the Takagi-Sugeno fuzzy systems, simulated anneal-ing, and fault detection methods.We have accepted thirty-six papers in this special issue.In the published papers, eight consider the stability andstabilization problems of stochastic systems. There are four-teen papers which discuss the problems of the controllerdesign and relevant optimization algorithms. Six articlesstudy the system modeling and identification methods. Onepaper focuses on the fault detection for wireless networkedcontrol systems with stochastic uncertainties and multipletime delays, and seven consider the state estimation andfiltering problems.The problems of stochastic stability and stabilizationproblems of Markovian jumping systems have been exten-sively studied bymany researchers, andmany relevant resultshave been made. The paper entitled “Sufficient conditionson the exponential stability of neutral stochastic differentialequations with time-varying delays” by Y. Tian and B. Chenconsiders the exponential stability in almost sure senseof the neutral stochastic differential equations with time-varying delays and the paper entitled “Delay-dependent robustexponential stability and H∞analysis for a class of uncertainMarkovian jumping system with multiple delays” by J. Xiadeals with the problem of robust exponential stability andH∞performance analysis for a class of uncertain Markovianjumping systems with multiple delays. The paper entitled“On input-to-state stability of impulsive stochastic systems withtime delays” by F. Yao et al. is concerned with pth momentinput-to-state stability and stochastic input-to-state stabilityof impulsive stochastic systems with time delays. The paperentitled “Absolute stability of a class of nonlinear singularsystems with time delay” by H.-B. Zeng et al. studies theabsolute stability for a class of nonlinear singular systemswith time delay. The paper entitled “Analysis and design ofHindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014, Article ID 582549, 3 pageshttp://dx.doi.org/10.1155/2014/5825492 Abstract and Applied Analysisnetworked control systems with randomMarkovian delays anduncertain transition probabilities” by L. Qiu et al. focuses onthe stability issue of discrete-time networked control systemswith random Markovian delays and uncertain transitionprobabilities. For the stochastic stabilization aspects, thepaper entitled “Finite-time boundedness for a class of delayedMarkovian jumping neural networks with partly unknowntransition probabilities” by L. Liang is concerned with theproblem of finite-time boundedness for a class of delayedMarkovian jumping neural networks with partly unknowntransition probabilities, and the paper entitled “Outputfeedback adaptive stabilization of uncertain nonholonomicsystems” by Y. Wu et al. investigates the problem of outputfeedback adaptive stabilization control design for a class ofnonholonomic chained systems. The paper entitled “Robustexponential stabilization of stochastic delay interval recurrentneural networks with distributed parameters and Markovianjumping by using periodically intermittent control” by J. Hu etal. considers a class of stochastic delay recurrent neural net-works with distributed parameters and Markovian jumping.In recent years, the research on control optimizationfor stochastic dynamic systems has received more andmore attention. For the H∞control aspects, the paperentitled “Finite-time H∞control for discrete-time Markovjump systems with actuator saturation” by B. Li and J. Zhaopresents the finite-time control problem for discrete-timeMarkov jump systems subject to saturating actuators, andthe paper entitled “Finite-time H∞control for a class ofdiscrete-time Markov jump systems with actuator saturationvia dynamic antiwindup design” by J. Zhao et al. deals withthe finite-time control problem for discrete-time Markovjump systems subject to saturating actuators. The paperentitled “Stochastic finite-time H∞performance analysis ofcontinuous-time systems with random abrupt changes” by B.Wang proposes the problem of H∞control performanceanalysis of continuous-time systems with random abruptchanges. The paper entitled “Robust finite-time H∞controlfor nonlinear Markovian jump systems with time delay underpartially known transition probabilities” by D. Yang andG. Zong considers the problem of robust finite-time H∞control for a class of nonlinearMarkovian jump systems withtime delay under partially known transition probabilities.The paper entitled “Nonfragile H∞control for stochasticsystems with Markovian jumping parameters and randompacket losses” by J. Wang and K. Zhang is concerned withthe nonfragile H∞control problem for stochastic systemswith Markovian jumping parameters and random packetlosses. The paper entitled “Finite-time control for Markovianjump systems with polytopic uncertain transition descriptionand actuator saturation” by Z. Tang addresses the finite-time 𝐿2-L∞control problems for Markovian jump systemswith time-varying delays, actuator saturation, and polytopicuncertain transition description; the paper entitled “Resilientrobust finite-time𝐿2-L∞controller design for uncertain neutralsystem with mixed time-varying delays” by X. Chen and S.He proposes the delay-dependent resilient robust finite-time𝐿2-L∞control problem of uncertain neutral time-delayedsystem. For the predictive control aspects, the paper entitled“A simplified predictive control of constrained Markov jumpsystem with mixed uncertainties” by Y. Yin et al. designs asimplified model predictive control algorithm for discrete-time Markov jump systems with mixed uncertainties; thepaper entitled “Predictive function optimization control for aclass of hydraulic servo vibration systems” by X. Feng et al. isconcernedwith the problemof predictive function control fora class of hydraulic vibration servo control systems.The paperentitled “Global multivariable control of permanent magnetsynchronousmotor formechanical elastic energy storage systemunder multiclass nonharmonic external disturbances” by Y.Yu et al. proposes a global multivariable control algorithmbased on nonlinear internalmodel principle undermulticlassexternal disturbances; the paper entitled “Feedforward andfeedback control performance assessment for nonlinear sys-tems” by Z.Wang and J. Chen proposes a performance assess-mentmethod for nonlinear feedforward and feedback controlsystems. For themultiagent systems control aspects, the paperentitled “Output feedback control for couple-group consensusof multiagent systems” by H. Zhao et al. deals with the couple-group consensus problem for multiagent systems via outputfeedback control; the paper entitled “Asynchronous gossip-based gradient-free method for multiagent optimization” byD. Yuan considers the constrained multiagent optimizationproblem; and the paper entitled “Control of multiagentsystems: a stochastic pinning viewpoint” G. Wang developsa stochastic pinning approach for multiagent systems toguarantee such systems being almost surely stable.Over the past few decades, the signal processing, estima-tion, and filtering problems have long been the mainstreamof research topics. For the filtering problems, the paper enti-tled “Structural stiffness identification based on the extendedKalman filter research” by F.Wang et al. develops an extendedKalman filter to identify the structural stiffness parameters,the paper entitled “Improved robust H∞filtering approachfor nonlinear systems” by J. Chen and H. Sun presents animproved design approach of robust H∞filter for a classof nonlinear systems described by the Takagi-Sugeno fuzzymodel, and the paper entitled “Delay-dependent robust 𝐿2-L∞filtering for a class of fuzzy stochastic systems” by Z. Liand X. Yang is concerned with the 𝐿2-L∞filtering problemfor a kind of Takagi-Sugeno’s fuzzy stochastic system withtime-varying delay and parameter uncertainties. For the stateestimation problems, the paper entitled “State estimation forwireless network control systemwith stochastic uncertainty andtime delay based on sliding mode observer” by P. Guo et al.considers the state estimation problems for a kind of wirelessnetwork control system with stochastic uncertainty and timedelay, whereas the paper entitled “State estimation for time-delay systems with Markov jump parameters and missingmeasurements” by Y. Tan et al. is concerned with the stateestimation problem for a class of time-delay systems withMarkovian jump parameters andmissingmeasurements.Thepaper entitled “Constants within error estimates for Legendre-Galerkin spectral approximations of control-constrained opti-mal control problems” by J. Zhou addresses the explicitformulae of constants within a posteriori error estimate foroptimal control problems, and the paper entitled “Optimalstate estimation for discrete-time Markov jump systems withmissing observations” by Q. Sun et al. is concerned with theAbstract and Applied Analysis 3optimal linear estimation for a class of direct-time Markovjump systems with missing observations. The paper entitled“Fault detection for wireless networked control systems withstochastic uncertainties and multiple time delays” by L. Ronget al. investigates the fault detection problem for a class ofwireless networked control systems.As is well known that the system modeling and identifi-cation are very useful in engineering applications, the paperentitled “Integration by parts andmartingale representation fora Markov chain” by T. K. Siu derives the integration-bypartsformulas for functions of fundamental jump processes relat-ing to a continuous-time, finite-state Markov chain usingthe Bismut measure change approach. The paper entitled“Generalized mutual synchronization between two controlledinterdependent networks” by Q. Xu et al. focuses on the gener-alized mutual synchronization between two controlled inter-dependent networks.The paper entitled “Cascading dynamicsof heterogenous scale-free networks with recovery mechanism”by S. Li et al. defines five kinds of weighting strategies toassign the external resources for recovering the edges fromcascading failures in heterogeneous scale-free networks. Thepaper entitled “Portfolio strategy of financial market withregime switching driven by geometric Le´vy process” by L. Zhouand Z. Wang studies the problem of a portfolio strategyfor financial market with regime switching driven by thegeometric Le´vy process. The paper entitled “Gsanular spacereduction to a 𝛽 multigranulation fuzzy rough set” by J. Zhouet al. further generalizes𝛽multigranulation rough set to fuzzyenvironment. The paper entitled “Boundary recognition bysimulating a diffusion process in wireless sensor networks” byD. Gu et al. proposes a distributed algorithm for boundaryrecognition in wireless sensor networks.Although the selected topics and published papers arenot a comprehensive representation of stochastic Markovianjumping systems, the authors represent the rich and many-faceted knowledge and we still hope the reader will find ourspecial issue very useful.AcknowledgmentsWe first express our great appreciation to all the authors ofthis special issue for their high quality contributions. All thereviewers’ efforts in reviewing the papers are also very greatlyacknowledged.Shuping HeZhengguang WuHao ShenYanyan YinQuanxin ZhuSubmit your manuscripts athttp://www.hindawi.comHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical Problems in EngineeringHindawi Publishing Corporationhttp://www.hindawi.comDifferential EquationsInternational Journal ofVolume 2014Applied MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical PhysicsAdvances inComplex AnalysisJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014OptimizationJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Operations ResearchAdvances inJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Function SpacesAbstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal of Mathematics and Mathematical SciencesHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014AlgebraDiscrete Dynamics in Nature and SocietyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Decision SciencesAdvances inDiscrete MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.comVolume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Stochastic AnalysisInternational Journal of

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