Jun Hu · Zidong Wang Huijun Gao Nonlinear Stochastic Systems with Network-Induced Phenomena Recursive Filtering and Sliding-Mode Design Nonlinear Stochastic Systems with Network-Induced Phenomena Jun Hu Zidong Wang • • Huijun Gao Nonlinear Stochastic Systems with Network-Induced Phenomena Recursive Filtering and Sliding-Mode Design 123 Jun Hu Huijun Gao Department of AppliedMathematics Research Instituteof IntelligentControl Harbin UniversityofScience andSystems andTechnology Harbin InstituteofTechnology Harbin Harbin China China Zidong Wang Department of InformationSystems andComputing BrunelUniversity Uxbridge Middlesex UK ISBN 978-3-319-08710-8 ISBN 978-3-319-08711-5 (eBook) DOI 10.1007/978-3-319-08711-5 LibraryofCongressControlNumber:2014943125 SpringerChamHeidelbergNewYorkDordrechtLondon (cid:2)SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. 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While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) This book is dedicated to the Dream Dynasty consisting of a group of bright people who have been to Brunel University of the UK to enjoy memorable research life by recursively filteringthenoisesandthendrivingthelifeto the happy sliding mode in finite time…… Preface Nonlinearity and stochasticity are ubiquitous features existing in almost all prac- tical systems that contribute significantly to the complexity of system modeling. Since the occurrence of the nonlinearity and stochasticity inevitably degrades the system performance and even leads to instability, the analysis and synthesis problems for nonlinear stochastic systems have long been the mainstream of research topics and much efforts have been made to deal with the nonlinear sto- chastic systems. Over the past decade, with the rapid developments of the net- worked control systems (NCSs), the design of controller/filter for nonlinear stochastic systems with network-induced phenomena has become a hot research focus that has attracted an increasing interest. This book is concerned with the recursive filtering and sliding mode design problems for several classes of discrete-time nonlinear stochastic systems with network-induced phenomena. The content of this book can be conceptually divi- ded into two parts. In the first part, we focus mainly on the recursive filter design problemsforsomeclassesoftime-varyingnonlinearstochasticsystemssubjectto random parameter matrices, multiple fading measurements, correlated noises, stochasticnonlinearities,missingmeasurements,quantizationeffects,probabilistic sensor delays, gain constraints, as well as sensor saturations. Some new filtering algorithms are developed in terms of the solutions to Riccati-like difference equations or difference linear matrix inequalities (DLMIs), which are suitable for recursive computations in online applications. Some theories and methodologies obtained are applied to design the filters for the target tracking systems, which show the promising applications of the proposed approaches. In the second part, the sliding mode control (SMC) and sliding mode observer (SMO) design problems are considered for several classes of nonlinear stochastic systems with randomly occurring uncertainties (ROUs), randomly occurring nonlinearities (RONs), time-varying delays, infinite distributed delays and Markovian jumping parameters. In this part, the new concept of ROUs is put forward and some new sliding surfaces are constructed for the addressed systems. Some sufficient conditionsareestablishedfortheslidingmodedesignthatcanbesolvedeasilyby using the semidefinite programming method. vii viii Preface Thecompendiousframeworkanddescriptionofthisbookaregivenasfollows. Chapter 1 introduces the recent advances on recursive filtering and sliding mode design for discrete nonlinear stochastic systems. Chapter 2 is concerned with the recursive filtering for time-varying nonlinear systems with stochastic nonlineari- ties,multiplemissingmeasurements,andquantizedeffects.Therecursivefiltering problemsareinvestigatedinChap.3fortime-varyingnonlinearsystemswherethe correlated noises, random parameter matrices, multiple fading measurements, probabilisticsensordelays,andgainconstraintsaretakenintoaccount.InChap.4, the probability-guaranteed H finite-horizon filtering problem is studied for a 1 class of time-varying nonlinear systems with randomly uncertain parameters and sensor saturations. The H SMO design problem is dealt with in Chap. 5 for a 1 class of nonlinear time-delay systems. Chapter 6 investigates the robust SMC problem for uncertain stochastic systems with time-delays, RONs, and stochastic nonlinearities, while Chap. 7 discusses the problem of robust SMC with mixed time-delays, ROUs, RONs, and Markovian jump parameters. Chapter 8 draws conclusions on this book and points out some possible research directions related to the work done in this book. This book is a research monograph whose intended audience is graduate and postgraduate students as well as researchers, serving as both a summary of the recent research results and a source offurther research directions. Harbin, China Jun Hu London, UK Zidong Wang Harbin, China Huijun Gao Acknowledgments We would like to acknowledge the help of many people who have been directly involvedinvariousaspectsoftheresearchleadingtothisbook.Specialthanksgo toProf.XiaohuiLiuandProf.LamprosStergioulasfromBrunelUniversityofthe UK, Prof. James Lam from the University of Hong Kong, Prof. Daniel W. C. Ho from City University of Hong Kong, and Prof. Yugang Niu from East China University of Science and Technology of China. We also extend our thanks to many colleagues who have offered support and encouragement throughout this research effort. In particular,we would like toacknowledge the contributions and friendly support from Bo Shen, Hongli Dong, Lifeng Ma, Yurong Liu, Jinling Liang, Guoliang Wei, Xiao He, Yao Wang, Derui Ding, Xiu Kan, Liang Hu, SunjieZhang,NianyinZeng,YangLiu,LeiZou,andQinyuanLiu.Finally,weare deeply indebted to our families for their never-ending understanding, unfailing encouragement and constant support when it was most required. ThewritingofthisbookwassupportedinpartbytheNationalNaturalScience Foundation of China under Grants 61329301, 61333012, 11301118, 61273156, 61134009, and 11271103, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and PhysicalSciencesResearchCouncil(EPSRC)oftheUK,theRoyalSocietyofthe UK, and the Alexander von Humboldt Foundation of Germany. The support of these organizations is much acknowledged. ix Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Research Background, Motivations, and Research Problems. . . . 1 1.1.1 Nonlinear Stochastic Systems. . . . . . . . . . . . . . . . . . . . 1 1.1.2 Network-Induced Phenomena. . . . . . . . . . . . . . . . . . . . 2 1.1.3 Nonlinear Filtering and Control . . . . . . . . . . . . . . . . . . 6 1.2 Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Recursive Filtering with Missing Measurements and Quantized Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1 Extended Kalman Filtering with Multiple Missing Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.2 Design of EKF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 Quantized Filtering with Missing Measurements and Multiplicative Noises. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.2 Design of Quantized Filter. . . . . . . . . . . . . . . . . . . . . . 39 2.3 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3 Recursive Filtering with Fading Measurements, Sensor Delays, and Correlated Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.1 Recursive Filtering with Random Parameter Matrices and Multiple Fading Measurements. . . . . . . . . . . . . . . . . . . . . 64 3.1.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.1.2 Design of Filter Gain. . . . . . . . . . . . . . . . . . . . . . . . . . 66 xi xii Contents 3.2 Gain-Constrained Recursive Filtering with Probabilistic Sensor Delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2.2 Design of Filter Gain with Gain Constraint . . . . . . . . . . 77 3.3 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4 Probability-Guaranteed H Finite-Horizon Filtering ‘ with Sensor Saturations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2 Main Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2.1 H Performance Analysis . . . . . . . . . . . . . . . . . . . . . . 107 1 4.2.2 Computational Algorithm. . . . . . . . . . . . . . . . . . . . . . . 112 4.3 An Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5 H Sliding Mode Observer Design for Nonlinear ‘ Time Delay Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.2 Design of SMO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2.1 Reachability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2.2 Performance Analysis of the Sliding Motion . . . . . . . . . 125 5.2.3 Computational Algorithm. . . . . . . . . . . . . . . . . . . . . . . 134 5.3 An Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 6 Sliding Mode Control with Time-Varying Delays and Randomly Occurring Nonlinearities. . . . . . . . . . . . . . . . . . . . 143 6.1 Robust SMC for Time Delay Systems with Randomly Occurring Nonlinearities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6.1.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.1.2 Design of SMC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.2 Robust H SMC for Time Delay Systems 1 with Stochastic Nonlinearities. . . . . . . . . . . . . . . . . . . . . . . . . 155 6.2.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 156 6.2.2 Sliding Motion Analysis . . . . . . . . . . . . . . . . . . . . . . . 157 6.2.3 Reachability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 164 6.3 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177