Control and Filtering for Semi-Markovian Jump Systems

208 Pages·2017·4.738 MB·English

by  Fanbiao Li, Peng Shi, Ligang Wu (auth.)

Studies in Systems, Decision and Control 81
Fanbiao Li
Peng Shi
Ligang Wu
Control and
Filtering
for Semi-
Markovian
Jump Systems
Studies in Systems, Decision and Control
Volume 81
Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail: [email protected]
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Fanbiao Li Peng Shi Ligang Wu
(cid:129) (cid:129)
Control and Filtering
for Semi-Markovian Jump
Systems
123
FanbiaoLi LigangWu
Schoolof Information Science Space Control andInertialTechnology
andEngineering ResearchCenter
Central SouthUniversity Harbin Institute of Technology
Changsha Harbin
China China
PengShi
Collegeof Engineering andScience
Victoria University
Melbourne
Australia
and
Schoolof Electrical andElectronic
Engineering
TheUniversity of Adelaide
Adelaide
Australia
ISSN 2198-4182 ISSN 2198-4190 (electronic)
Studies in Systems,DecisionandControl
ISBN978-3-319-47198-3 ISBN978-3-319-47199-0 (eBook)
DOI 10.1007/978-3-319-47199-0
LibraryofCongressControlNumber:2016953297
©SpringerInternationalPublishingAG2017
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To my parents and Yewen
—Fanbiao Li
To Fengmei, Lisa and Michael
—Peng Shi
To Jingyan and Zhixin
—Ligang Wu
Preface
In practice, a large class of physical systems has variable structures subject to
randomchanges.Thesemayresultfromabruptphenomenasuchascomponentand
interconnection failures, parameters shifting, tracking, and the time required to
measure some of the variables at different stages. Systems with this character may
be modeled as hybrid ones; that is, to the continuous state variable, a discrete
random variable called the mode, or regime, is appended. The mode describes the
randomjumpsofthesystemparametersandtheoccurrenceofdiscontinuities.Such
a system model is useful particularly since it allows the decision maker to cope
adequatelywiththediscreteeventsthatdisruptand/orchangethenormaloperation
of a system significantly, by using the knowledge of their occurrence and the
statisticalinformationontherateatwhichtheseeventstakeplace.Markovianjump
systems (MJS), with its powerful modeling capability in application areas such as
the aerospace industry, industrial processes, biomedical industry, and socioeco-
nomics,haveprovedtobeofvitalimportanceasatypicalclassofhybriddynamical
system. However, MJS have many limitations in applications, since the jump time
in MJS is subject to exponential distribution or geometric distribution in continu-
ous- and discrete-time domains, respectively. So, the results obtained for the MJS
are intrinsically conservative due to constant transition rates. Compared with the
MJS,semi-Markovianjumpsystems(S-MJS)arecharacterizedbyafixedmatrixof
transition probabilities and a matrix of sojourn time probability density functions.
Due to their relaxed conditions on the probability distributions, S-MJS have much
broader applications than the conventional MJS. Thus, this area of research is
significant because of both its theoretical and practical values.
This book aims to present up-to-date research developments and novel
methodologiesonS-MJS.Thecontentofthisbookcanbedividedintothreeparts:
Part I is focused on stability analysis and control of the considered S-MJS, Part II
puts the emphasis on fault detection and filtering of S-MJS, while Part III sum-
marizes the results of the book. These methodologies provide a framework for
stabilityandperformanceanalysis,robustcontrollerdesign,robustfilterdesign,and
fault detection for the considered systems. The main contents of Part I include the
following: Chapter 2 is concerned with stochastic stability of S-MJS with
vii
viii Preface
mode-dependent delays; Chapter 3 studies the constrained regulation problem of
singular S-MJS; Chapter 4 addresses the state estimation and sliding mode control
problems of S-MJS with mismatched uncertainties; and Chap. 5 investigates the
quantizeddynamicoutputfeedbackcontrolofnonlinearS-MJS.Themaincontents
of Part II include the following: Chapter 6 is concerned with the neural
network-based passive filter design for delayed neutral-type S-MJS; Chapter 7
studies event-triggered fault detection filtering problem for sojourn
information-dependent S-MJS; Chapter 8 addresses the fault detection filtering for
S-MJS via T-S fuzzy approach; Chapter 9 investigates the fault detection problem
for underactuated manipulators modeled by MJS; and Chap. 10 summarizes the
results of the book and discusses some future works.
This book is a research monograph whose intended audience is graduate and
postgraduate students as well as researchers. Prerequisite to reading this book is
elementary knowledge on mathematics, matrix theory, probability, optimization
techniques, and control system theory.
Changsha, China Fanbiao Li
Adelaide, Australia Peng Shi
Harbin, China Ligang Wu
July 2016
Acknowledgments
There are numerous individuals without whose constructive comments, useful
suggestions, and wealth of ideas this monograph could not have been completed.
Special thanks go to Prof. Michael V. Basin from Autonomous University,
Prof. Cheng-Chew Lim from the University of Adelaide, and Profs. Weihua Gui
and Chunhua Yang from Central South University, for their valuable suggestions,
constructive comments, and support. Next, our acknowledgements go to many
colleagues who have offered support and encouragement throughout this research
effort. In particular, we would like to acknowledge the contributions from Rongni
YangandXiaojieSu.Thanksalsogotoourstudents,ZhongruiHu,HuiyanZhang,
andHongjunYu,fortheircommentary.Finally,wewouldliketothanktheeditors
at Springer for their professional and efficient handling of this project.
This work was partially supported by the Australian Research Council
(DP140102180,LP140100471),theNationalNaturalScienceFoundationofChina
(61603417, 61573112, 61525303, U1509217), the Top-Notch Young Talents
ProgramofChina(LigangWu),theHeilongjiangOutstandingYouthScienceFund
(JC201406),theFok YingTungEducation Foundation(141059),theSelf-Planned
Task of State Key Laboratory of Robotics and System (HIT) (201505B), the
Foundation for Innovative Research Groups of the National Natural Science
Foundation of China (61321003), the Innovation-Driven Plan in Central South
University (2015cx007), and the Heilongjiang Youth Science Fund (QC2016082).
ix
Contents
1 Introduction... .... .... ..... .... .... .... .... .... ..... .... 1
1.1 Analysis and Control of MJS.. .... .... .... .... ..... .... 1
1.1.1 Stability Analysis of MJS... .... .... .... ..... .... 2
1.1.2 Control and Filtering of MJS .... .... .... ..... .... 6
1.2 Analysis and Control of S-MJS .... .... .... .... ..... .... 14
1.2.1 Literature Review of S-MJS . .... .... .... ..... .... 14
1.2.2 Mathematical Descriptions and Basic Concepts.... .... 15
1.3 Outline of the Book ..... .... .... .... .... .... ..... .... 19
References. .... .... .... ..... .... .... .... .... .... ..... .... 22
Part I Stability and Control
2 Stochastic Stability of Semi-Markovian Jump Systems . ..... .... 31
2.1 Introduction .. .... ..... .... .... .... .... .... ..... .... 31
2.2 System Description and Preliminaries.... .... .... ..... .... 31
2.3 Main Results.. .... ..... .... .... .... .... .... ..... .... 32
2.4 Illustrative Example ..... .... .... .... .... .... ..... .... 42
2.5 Conclusion ... .... ..... .... .... .... .... .... ..... .... 45
References. .... .... .... ..... .... .... .... .... .... ..... .... 45
3 Constrained Regulation of Singular Semi-Markovian
Jump Systems . .... .... ..... .... .... .... .... .... ..... .... 47
3.1 Introduction .. .... ..... .... .... .... .... .... ..... .... 47
3.2 System Description and Preliminaries.... .... .... ..... .... 48
3.3 Main Results.. .... ..... .... .... .... .... .... ..... .... 53
3.3.1 Full-Column Rank Solutions. .... .... .... ..... .... 53
3.3.2 Full-Row Rank Solutions ... .... .... .... ..... .... 57
3.3.3 A Heuristic Algorithm for Constrained Regulation
Problem.... ..... .... .... .... .... .... ..... .... 60
3.4 Simulation Results . ..... .... .... .... .... .... ..... .... 61
3.5 Conclusion ... .... ..... .... .... .... .... .... ..... .... 63
References. .... .... .... ..... .... .... .... .... .... ..... .... 64
xi