Nonlinear Stochastic Systems with Network-Induced Phenomena: Recursive Filtering and Sliding-Mode Design

230 Pages·2015·5.478 MB·English

by  Jun Hu, Zidong Wang, Huijun Gao (auth.)

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
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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