Control Synthesis for Semi-Markovian Switching Systems

227 Pages·2023·6.056 MB·English

by  Wenhai Qi, Guangdeng Zong

Studies in Systems, Decision and Control 465
Wenhai Qi
Guangdeng Zong
Control Synthesis
for Semi-Markovian
Switching Systems
Studies in Systems, Decision and Control
Volume 465
Series Editor
Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences,
Warsaw, Poland
The series “Studies in Systems, Decision and Control” (SSDC) covers both new
developments and advances, as well as the state of the art, in the various areas of
broadly perceived systems, decision making and control–quickly, up to date and
with a high quality. The intent is to cover the theory, applications, and perspec-
tives on the state of the art and future developments relevant to systems, decision
making, control, complex processes and related areas, as embedded in the fields
of engineering, computer science, physics, economics, social and life sciences, as
well as the paradigms and methodologies behind them. The series contains mono-
graphs, textbooks, lecture notes and edited volumes in systems, decision making
and control spanning the areas of Cyber-Physical Systems, Autonomous Systems,
Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biolog-
ical Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems,
Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems,
Robotics, Social Systems, Economic Systems and other. Of particular value to both
the contributors and the readership are the short publication timeframe and the world-
wide distribution and exposure which enable both a wide and rapid dissemination of
research output.
Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago.
All books published in the series are submitted for consideration in Web of Science.
·
Wenhai Qi Guangdeng Zong
Control Synthesis
for Semi-Markovian
Switching Systems
Wenhai Qi Guangdeng Zong
School of Engineering School of Control Science and Engineering
Qufu Normal University Tiangong University
Rizhao, Shandong, China Tianjin, China
ISSN 2198-4182 ISSN 2198-4190 (electronic)
Studies in Systems, Decision and Control
ISBN 978-981-99-0316-0 ISBN 978-981-99-0317-7 (eBook)
https://doi.org/10.1007/978-981-99-0317-7
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
Singapore Pte Ltd. 2023
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse
of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and
transmission or information storage and retrieval, electronic adaptation, computer software, or by similar
or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors, and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or
the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.
The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,
Singapore
Preface
Most of the physical systems in the actual operation may be affected by random
parameters, which will lead to sudden changes in the system structure. These
changes may suffer from sudden events, such as random component failures,
changing subsystem interconnection, unexpected events, and uncontrolled config-
uration changes. Then, the above system models cannot be accurately described by
the traditional system, which can be characterized by Markovian switching systems.
As a popular type of hybrid system, Markovian switching systems consist of some
subsystems described by differential equations or difference equations and random
switching rules among them. Because of a good engineering background, Marko-
vian switching systems find wide applications in many complex dynamic systems
including energy systems, macroeconomic models, networked control systems, fault-
tolerant systems, manufacturing systems, and sensor network systems. In these
circumstances, more and more experts have begun to study Markovian switching
systems from different disciplines, thus promoting the rapid development of the
corresponding theory.
It is well known that the transition rate plays an important role in the dynamic
characteristics and is subject to the probability distribution function of the sojourn
time. For Markovian switching systems, the sojourn time follows a unique memo-
ryless exponential distribution. In such circumstances, the transition rate becomes
time-invariant only related to the latest mode and is independent of sojourn time,
which greatly limits the practical application scope of Markovian switching systems.
Compared with Markovian switching systems, the sojourn time in semi-Markovian
switching systems obeys a more general nonexponential distribution including
Weibull distribution, phase-type distribution, Gaussian distribution, and so on, which
leads to the time-varying characteristic of the transition rate matrix and brings
both challenges and chances to the analysis and synthesis of dynamics. It should
be pointed out that the traditional Markovian switching systems are known as a
special class of semi-Markovian switching systems that can better model the dynamic
systems subject to inevitable stochastic changes. Semi-Markovian switching systems
have many applications in various fields of practical engineering, such as sliding
v
vi Preface
mode control, adaptive control, event-triggered control, finite-time control, and fault
detection.
In the past decades, the control synthesis for Markovian switching systems has
been intensively investigated and has attracted increasing attention. Although a large
number of the corresponding works have been developed from various disciplines,
there still exist many fundamental problems with less well understanding. In partic-
ular, there still lacks a unified framework to cope with the issue of control synthesis
for semi-Markovian switching systems. This motivates us to write related work.
The monograph aims to present up-to-date research developments and refer-
ences on the control synthesis for stochastic switching systems subject to the semi-
Markovian process. Owing to the particularity of semi-Markovian switching systems,
many previous approaches for traditional Markovian switching systems cannot be
extended to semi-Markovian switching systems, which makes analysis and synthesis
of semi-Markovian switching systems full of challenges. By using multiple semi-
Markovian Lyapunov function approaches, a basic theoretical framework is formed
towards the issue of control synthesis for semi-Markovian switching systems. The
book can be used for researchers to carry out studies on semi-Markovian switching
systems and is suitable for graduate students of control theory and engineering. It
may also be a valuable reference for control design of stochastic switching systems
by engineers.
The contents of the book are divided into 12 chapters which contain several inde-
pendent yet related topics, and they are organized as follows. Chapter 1 introduces
some basic background knowledge on semi-Markovian switching systems, and also
describes the main work of the book. Chapter 2 considers the problem of sliding
mode control law for semi-Markovian switching systems with signal quantization.
Chapters 3 and 4 address the problems of stochastic stability and finite-time reach-
ability for stochastic semi-Markovian switching systems and stochastic singular
semi-Markovian switching systems via sliding mode control approach. Chapter 5
gives theoretical developments in detail for finite-time sliding mode control of semi-
Markovian switching systems with quantized measurement. Chapters 6 and 7 study
adaptive event-triggered sliding mode control for semi-Markovian switching systems
and finite-time synchronization for delayed semi-Markovian switching neural
networks with quantized measurement. Sliding mode control problem for fuzzy
semi-Markovian switching systems is discussed in Chaps. 8 and 9. The specified
discrete-time sliding mode control is synthesized for discrete-time semi-Markovian
switching systems with denial-of-service attacks through a discrete-time semi-
Markovian kernel in Chap. 10. The sliding mode control issue is addressed for
networked semi-Markovian switching systems with deception attacks in Chap. 11.
Finally, Chap. 12 concludes some future study directions related to the contents of
the book.
Rizhao, China Wenhai Qi
November 2022 Guangdeng Zong
Acknowledgements
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. Wei Xing Zheng, Western Sydney University; Prof. Yang
Shi, University of Victoria; Prof. Ju H. Park, Yeungnam University; Prof. Jinde Cao,
Southeast University; Prof. Hamid Reza Karimi, Politecnico di Milano and Prof.
Xianwen Gao, Northeastern University, for their valuable suggestions, constructive
comments, and support. Next, our acknowledgments go to many colleagues who
have offered support and encouragement throughout this research effort. Finally, the
authors would like to express their sincere gratitude to the editors of the book for
their time and kind help.
The monograph was supported in part by the National Natural Science Foundation
of China (62073188), the Postdoctoral Science Foundation of China (2022T150374),
and the Natural Science Foundation of Shandong (ZR2021MF083).
Rizhao, China Wenhai Qi
November 2022 Guangdeng Zong
vii
Contents
1 Introduction .................................................. 1
1.1 Background ............................................. 1
1.2 Stability Analysis for S-MSSs .............................. 3
1.2.1 Stability for Stochastic S-MSSs ...................... 3
1.2.2 Stability for Continuous-Time Linear S-MSSs ......... 6
1.2.3 Stability for Discrete-Time Linear S-MSSs ............ 7
1.3 Control Synthesis for S-MSSs .............................. 9
1.3.1 Control and Filtering for S-MSSs .................... 11
1.3.2 Sliding Mode Control for S-MSSs .................... 13
1.3.3 Finite-Time Control for S-MSSs ..................... 15
1.3.4 Event-Triggered Control for S-MSSs ................. 17
1.4 Organization of the Book .................................. 19
References .................................................... 20
2 Quantized Sliding Mode Control ............................... 29
2.1 Introduction ............................................. 29
2.2 Problem Statements and Preliminaries ....................... 30
2.3 Stochastic Stability Analysis ............................... 32
2.4 Reachability Analysis ..................................... 36
2.5 Simulation .............................................. 37
2.6 Conclusion .............................................. 39
References .................................................... 40
3 Sliding Mode Control Under Stochastic Disturbance ............. 43
3.1 Introduction ............................................. 43
3.2 Problem Statements and Preliminaries ....................... 44
3.3 Sliding Mode Control Law Design .......................... 46
3.4 Stochastic Stability Analysis ............................... 46
3.5 Reachability Analysis ..................................... 53
ix
x Contents
3.6 Simulation .............................................. 56
3.7 Conclusion .............................................. 58
References .................................................... 59
4 Sliding Mode Control Under Stochastic Disturbance
and Singularity ............................................... 61
4.1 Introduction ............................................. 61
4.2 Problem Statements and Preliminaries ....................... 62
4.3 Sliding Mode Control Law Design .......................... 63
4.4 Stochastic Admissibility Analysis .......................... 64
4.5 Reachability Analysis ..................................... 71
4.6 Simulation .............................................. 73
4.7 Conclusion .............................................. 76
References .................................................... 76
5 Finite-Time Sliding Mode Control Under Quantization ........... 79
5.1 Introduction ............................................. 79
5.2 Problem Statements and Preliminaries ....................... 80
5.3 Sliding Mode Control Law Design .......................... 83
5.4 Finite-Time Boundedness Analysis over Reaching Phase
Within [0, T ∗] ........................................... 85
5.5 Finite-Time Boundedness Analysis over Sliding Motion
Phase Within [T ∗, T ] ..................................... 89
5.6 Gain Matrix Design ...................................... 93
5.7 Simulation .............................................. 96
5.8 Conclusion .............................................. 99
References .................................................... 100
6 Adaptive Event-Triggered Sliding Mode Control ................. 103
6.1 Introduction ............................................. 103
6.2 Problem Statements and Preliminaries ....................... 104
6.3 Stochastic Stability Analysis ............................... 109
6.4 Reachability Analysis ..................................... 115
6.5 Simulation .............................................. 116
6.6 Conclusion .............................................. 120
References .................................................... 120
7 Finite-Time Synchronization ................................... 123
7.1 Introduction ............................................. 123
7.2 Problem Statements and Preliminaries ....................... 124
7.3 Finite-Time Synchronization ............................... 127
7.4 Simulation .............................................. 136
7.5 Conclusion .............................................. 140
References .................................................... 141