Protocol-Based Sliding Mode Control: 1D and 2D System Cases

299 Pages·2022·19.608 MB·English

by  Jun Song, Zidong Wang, Yugang Niu

Protocols-Based Sliding
Mode Control
This book discusses the Sliding Mode Control (SMC) problems of networked
control systems (NCSs) under various communication protocols including static/
dynamic/periodic event-triggered mechanism, and stochastic communication,
Round-Robin, weighted try-once-discard, multiple-packet transmission, and the
redundant channel transmission protocol.  The super-twisting algorithm and the
extended-state-observer-based SMC scheme are investigated in this book for
suppressing chattering. Besides, the SMC designs for one-dimensional (1-D) and
two-dimensional (2-D) NCSs are illustrated as well.
Features:
• Captures recent advances of theories, techniques, and applications of net-
worked sliding mode control from an engineering-oriented perspective.
• Includes new design ideas and optimization techniques of networked sliding
mode control theory.
• Provides advanced tools to apply networked sliding mode control techniques
in the practical applications.
• Discusses some new tools to the engineering applications while dealing with
the model uncertainties and external disturbances.
This book aims at Researchers and professionals in Control Systems, Computer
Networks, Internet of Things, and Communication Systems.

Protocols-Based Sliding
Mode Control
1-D and 2-D System Cases
Jun Song
Zidong Wang
Yugang Niu
First edition published 2023
by CRC Press
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© 2023 Jun Song, Zidong Wang and Yugang Niu
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ISBN: 9781032313870 (hbk)
ISBN: 9781032313887 (pbk)
ISBN: 9781003309499 (ebk)
DOI: 10.1201/9781003309499
Typeset in CMR10
by KnowledgeWorks Global Ltd.
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
To our families and our friends.

Contents
List of Figures xi
List of Tables xv
Preface xvii
Author’s Biography xix
Acknowledgments xxiii
Symbols xxv
1 Introduction 1
1.1 Sliding Mode Control . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Network Communication Protocols . . . . . . . . . . . . . . 10
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
PART I: 1-D System Case 21
2 H Sliding Mode Control Under Stochastic Communication
∞
Protocol 23
2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 Analysis of reachability . . . . . . . . . . . . . . . . . 27
2.2.2 Analysis of stochastic stability with H performance 29
∞
2.2.3 Solving algorithm. . . . . . . . . . . . . . . . . . . . . 32
2.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 Static Output-Feedback Sliding Mode Control Under
Round-Robin 41
3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.1 Token-dependent static output-feedback SMC law . . 44
3.2.2 Analysis of the asymptotic stability . . . . . . . . . . 45
3.2.3 Analysis of the reachability . . . . . . . . . . . . . . . 49
3.2.4 Solving algorithm. . . . . . . . . . . . . . . . . . . . . 52
vii
viii Contents
3.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 Observer-Based Sliding Mode Control Under Weighted
Try-Once-Discard Protocol 61
4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2.1 Token-dependent state-saturated observer . . . . . . . 65
4.2.2 Token-dependent sliding mode controller . . . . . . . . 65
4.2.3 Analysis of the asymptotic stability . . . . . . . . . . 66
4.2.4 Analysis of the reachability . . . . . . . . . . . . . . . 69
4.2.5 Solving algorithm. . . . . . . . . . . . . . . . . . . . . 71
4.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Asynchronous Sliding Mode Control Under Static
Event-Triggered Protocol 79
5.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 80
5.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.2.1 Designing of sliding surface and sliding mode controller 82
5.2.2 Analysis of sliding mode dynamics . . . . . . . . . . . 83
5.2.3 Analysis of reachability . . . . . . . . . . . . . . . . . 86
5.2.4 Synthesis of SMC law . . . . . . . . . . . . . . . . . . 90
5.2.5 Solving algorithm. . . . . . . . . . . . . . . . . . . . . 93
5.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 Sliding Mode Control Under Dynamic Event-Triggered
Protocol 101
6.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.1 A novel sliding surface . . . . . . . . . . . . . . . . . . 103
6.2.2 Dynamic event-triggered SMC law . . . . . . . . . . . 103
6.2.3 The reachability of sliding surface . . . . . . . . . . . 104
6.2.4 The stability of sliding mode dynamics . . . . . . . . 106
6.2.5 Further discussions . . . . . . . . . . . . . . . . . . . . 109
6.2.5.1 Special case: Static event-triggered SMC of
slow-sampling SPSs . . . . . . . . . . . . . . 109
6.2.5.2 Convergence of the quasi-sliding motion . . . 112
6.2.6 Solving algorithm. . . . . . . . . . . . . . . . . . . . . 112
6.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Contents ix
7 Reliable Sliding Mode Control Under Redundant Channel
Transmission Protocol 117
7.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 117
7.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2.1 Sliding function and sliding mode controller . . . . . . 120
7.2.2 MSEUB of closed-loop system. . . . . . . . . . . . . . 123
7.2.3 The reachability of sliding surface . . . . . . . . . . . 126
7.2.4 Solving algorithm. . . . . . . . . . . . . . . . . . . . . 130
7.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8 State-Saturated Sliding Mode Control Under
Multiple-Packet Transmission Protocol 139
8.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 140
8.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.2.1 Sliding function and sliding mode controller . . . . . . 143
8.2.2 Analysis of sliding mode dynamics . . . . . . . . . . . 145
8.2.3 Analysis of reachability . . . . . . . . . . . . . . . . . 147
8.2.4 Synthesis of SMC law . . . . . . . . . . . . . . . . . . 151
8.2.5 Solving algorithm. . . . . . . . . . . . . . . . . . . . . 153
8.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
9 ESO-Based Terminal Sliding Mode Control Under Periodic
Event-Triggered Protocol 161
9.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 162
9.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.2.1 The design of ESO . . . . . . . . . . . . . . . . . . . . 163
9.2.2 Design of periodic event-triggered TSMC based on ESO 165
9.2.3 Estimation of actual bound for (cid:107)e(t)(cid:107) . . . . . . . . . 167
9.2.4 Selection criterion for periodic sampling period λ . . . 169
9.2.5 Reachability and stability . . . . . . . . . . . . . . . . 170
9.2.6 Solving algorithm . . . . . . . . . . . . . . . . . . . . 173
9.3 Simulation and Experiment . . . . . . . . . . . . . . . . . . . 177
9.3.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . 177
9.3.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . 183
9.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
PART II: 2-D System Case 191
10 2-D Sliding Mode Control Under Event-Triggered Protocol 193
10.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 194
10.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
10.2.1 2-D sliding surface . . . . . . . . . . . . . . . . . . . . 195
10.2.2 Design of 2-D event generator . . . . . . . . . . . . . . 195
10.2.3 Stability of sliding mode dynamics . . . . . . . . . . . 198