Nonlinear Stochastic Systems with Incomplete Information: Filtering and Control

253 Pages·2013·2.804 MB·English

by  Bo Shen, Zidong Wang, Huisheng Shu (auth.)

Nonlinear Stochastic Systems
with Incomplete Information
Bo Shen (cid:2) Zidong Wang (cid:2) Huisheng Shu
Nonlinear
Stochastic Systems
with Incomplete
Information
Filtering and Control
BoShen HuishengShu
SchoolofInform.Science&Technol. SchoolofInform.Science&Technol.
DonghuaUniversity DonghuaUniversity
Shanghai,China,People’sRepublic Shanghai,China,People’sRepublic
ZidongWang
Dept.ofInformation
Systems&Computing
BrunelUniversity
Uxbridge,UK
ISBN978-1-4471-4913-2 ISBN978-1-4471-4914-9(eBook)
DOI10.1007/978-1-4471-4914-9
SpringerLondonHeidelbergNewYorkDordrecht
LibraryofCongressControlNumber:2013930011
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This book is dedicated to the Dream Dynasty
consistingofagroupofbrightpeoplewhoare
alwayssmilingattheinherentlynonlinearyet
stochasticlifebyfilteringandthencontrolling
theincompleteinformation...
Preface
Recently,networkedcontrolsystems(NCSs)havegraduallybecomeanactivearea
ofresearchduetotheiradvantagesinmanyaspectssuchaslowcost,reducedweight
andpowerrequirements,simpleinstallationandmaintenance,aswellashighreli-
ability. It is well known that the devices in networks are mutually connected via
communicationcablesoflimitedcapacity.Therefore,somenewchallengingissues
have inevitably emerged, for example, network-induced time delay, data missing
(alsocalledpacketdropoutormissingmeasurement),andquantizationeffect,allof
whichshouldbetakenintoaccountinordertoachievetherequiredperformanceof
theNCSs.Theseissuesareusuallyreferredtoasincompleteinformation.
Inthisbook,wediscussthefilteringandcontrolproblemsforseveralclassesof
nonlinearstochasticsystemswithincompleteinformation.Thecausesofincomplete
informationconsideredhereincludemissingmeasurements,sensordelays,quanti-
zationeffects,sensor saturations,and signalsampling.The contentof this bookis
conceptualy divided mainly into three parts. In the first part, we focus on the H∞
filteringandcontrolproblemsforsomeverygeneralclassesofnonlinearstochastic
discrete-time systems subject to missing measurements, quantization effects, and
randomlyvaryingsensordelays.Somesufficientconditionsarederivedfortheex-
istenceofthedesiredfiltersandcontrollersintermsoftheHamilton–Jacobi–Isaacs
(HJI) inequalities. The robust H∞ filtering problems are considered in the second
part for several special classes of nonlinear stochastic systems. In this part, some
novel notions, including randomly occurring nonlinearities (RONs) and randomly
occurring sensor saturations (ROSSs), are first put forward. Then, we develop a
newfilteringtechniquefortheconsiderednonlinearstochasticsystemswithRONs,
ROSSs,andpacketdropouts.Inthethirdpart,thetheoryandtechniquedevelopedin
previouspartsareappliedtodealwithsomeissuesinbothsensornetworksandcom-
plexnetworks,andsomesampled-data-basedcontrollersandfiltersaredesigned.
Thecompendiousframeanddescriptionofthebookaregivenasfollows.Chap-
ter 1 introduces the recent advances on filtering and control with incomplete in-
formation and the outline of the book. Chapter 2 is concerned with the quantized
H∞ control problem for a class of nonlinear stochastic time-delay network-based
systemswithprobabilisticdatamissing.TheH∞filteringproblemsareinvestigated
vii
viii Preface
forageneralclassofnonlineardiscrete-timestochasticsystemswithmissingmea-
surements and randomly varying sensor delays in Chap. 3. In Chaps. 4 and 5, the
robustH∞finite-horizonfilteringproblemisaddressedforaspecialclassofnonlin-
eardiscrete-time-varyingstochasticsystemswherequantizationeffects,successive
packetdropouts,RONs,andROSSsaretakenintoaccount.Chapters6,7,and8in-
vestigatethedistributedH∞-consensusfilteringprobleminsensornetworks,while
Chaps. 9 and 10 discuss the synchronization and state estimation problems for
stochasticcomplexnetworks.
This book is a research monograph whose intended audience is graduate and
postgraduatestudentsaswellasresearchers.
Shanghai,China BoShen
London,UK ZidongWang
Shanghai,China HuishengShu
Acknowledgements
We would like to acknowledge the help of many people during the writing of this
book. We wish to express our heartfelt gratitude to Professor Xiaohui Liu from
Brunel University of the UK for his continued encouragement. Without his assis-
tanceandpersistenthelpthisbookwouldnothavebeenpossible.Inthiswewould
also like to include our gratitude to Professor James Lam from the University of
HongKongandProfessorDanielHofromCityUniversityofHongKongfortheir
strongsupport.Theinformalsupportandencouragementofmanyfriendshasbeen
indispensable, and we would like particularly to acknowledge the contribution of
YurongLiu,JinlingLiang,GuoliangWei,XiaoHe,YaoWang,HongliDong,Lifeng
Ma,RongniYang,JianxinFeng,JunHu,DeruiDing,andLiangHu.Finally,weare
deeply indebted to our families for their understanding, endless patience, and en-
couragementwhenitwasmostrequired.
ix
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 IncompleteInformation . . . . . . . . . . . . . . . . . . . 3
1.1.2 ComplexSystems . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Quantized H∞ Control for Time-Delay Systems with Missing
Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 SomeSpecialCases . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4 IllustrativeExamples. . . . . . . . . . . . . . . . . . . . . . . . . 44
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3 H∞ FilteringwithMissingMeasurementsandRandomlyVarying
SensorDelays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3 NonlinearH∞ FilteringwithLinearFilters . . . . . . . . . . . . 61
3.4 H∞ FilteringwithRandomlyVaryingSensorDelays . . . . . . . . 64
3.4.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . 64
3.4.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5 IllustrativeExamples. . . . . . . . . . . . . . . . . . . . . . . . . 70
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 FilteringwithRandomlyOccurringNonlinearities,Quantization,
andPacketDropouts . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2 PerformanceAnalysisofH∞ Filters . . . . . . . . . . . . . . . . 81
4.3 DesignofRobustH∞ Filters . . . . . . . . . . . . . . . . . . . . 84
4.4 RobustH∞ FilteringforTime-VaryingSystemswithMRONsand
SPDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
xi
xii Contents
4.4.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . 88
4.4.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.5 IllustrativeExamples. . . . . . . . . . . . . . . . . . . . . . . . . 94
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5 H∞ FilteringwithRandomlyOccurringSensorSaturationsand
MissingMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3 AnIllustrativeExample . . . . . . . . . . . . . . . . . . . . . . . 114
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6 DistributedH∞-ConsensusFilteringinSensorNetworks . . . . . . . 119
6.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 DistributedH∞-ConsensusFiltering . . . . . . . . . . . . . . . . 123
6.3 RobustDistributedH∞-ConsensusFilteringforUncertain
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.3.1 Norm-BoundedUncertainties . . . . . . . . . . . . . . . . 129
6.3.2 PolytopicUncertainties . . . . . . . . . . . . . . . . . . . 131
6.4 IllustrativeExamples. . . . . . . . . . . . . . . . . . . . . . . . . 133
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7 DistributedH∞ FilteringforPolynomialSystemsinSensor
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 139
7.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.3 AnIllustrativeExample . . . . . . . . . . . . . . . . . . . . . . . 149
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8 Sampled-DataApproachtoDistributedH∞ FilteringinSensor
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8.3 AnIllustrativeExample . . . . . . . . . . . . . . . . . . . . . . . 172
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
9 Sampled-DataSynchronizationControlandStateEstimationfor
ComplexNetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 178
9.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
9.3 Sampled-DataH∞ FilteringforStochasticGeneticRegulatory
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
9.3.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . 189
9.3.2 MainResults . . . . . . . . . . . . . . . . . . . . . . . . . 193
9.4 IllustrativeExamples. . . . . . . . . . . . . . . . . . . . . . . . . 202
9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Contents xiii
10 BoundedH∞ SynchronizationandStateEstimationforComplex
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
10.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . 211
10.2 BoundedH∞-Synchronization . . . . . . . . . . . . . . . . . . . 213
10.3 Finite-HorizonH∞ StateEstimation . . . . . . . . . . . . . . . . 217
10.4 IllustrativeExamples. . . . . . . . . . . . . . . . . . . . . . . . . 222
10.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
11 ConclusionsandFutureWork . . . . . . . . . . . . . . . . . . . . . . 233
11.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
11.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245