Control over Communication Networks Modeling, Analysis, and Design of Networked Control Systems and Multi-Agent Systems over Imperfect Communication Channels

by Zheng, Jianying; Xu, Liang; Hu, Qinglei; Xie, Lihua

• ISBN13: 9781119885795
• ISBN10: 1119885795
• eBook ISBN(s): 9781119885818
• Edition: 1st
• Format: Hardcover
• Copyright: 2023-05-16
• Publisher: Wiley-IEEE Press
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Summary

Control over Communication Networks

Advanced and systematic examination of the design and analysis of networked control systems and multi-agent systems

Control Over Communication Networks provides a systematic and nearly self-contained description of the analysis and design of networked control systems (NCSs) and multi-agent systems (MASs) over imperfect communication networks, with a primary focus on fading channels and delayed channels. The text characterizes the effect of communication channels on the stability and performance of NCSs, and further studies the joint impact of communication channels and network topology on the consensus of MASs.

By integrating communication and control theory, the four highly-qualified authors present fundamental results concerning the stabilization of NCSs over power-constrained fading channels and Gaussian finite-state Markov channels, linear-quadratic optimal control of NCSs with random input gains, optimal state estimation with intermittent observations, consensus of MASs with communication delay and packet dropouts, and synchronization of delayed Vicsek models.

Simulation results are given in each chapter to demonstrate the developed analysis and synthesis approaches. The references are comprehensive and up-to-date, enabling further study for readers.

Topics covered in Control Over Communication Networks include:

• Basic foundational knowledge, including control theory, communication theory, and graph theory, to enable readers to understand more complex topics
• The stabilization, optimal control, and remote state estimation problems of linear systems over channels with fading, signal-to-noise constraints, or intermittent measurements
• Consensus problems of MASs over fading/delayed channels, with directed and undirected communication graphs

Control Over Communication Networks provides a valuable unified platform for understanding the analysis and design of NCSs and MASs for researchers, control engineers working on control systems over communication networks, and mechanical engineers working on unmanned systems. Preliminary knowledge of linear system theory and matrix analysis is required.

Author Biography

Jianying Zheng is an Associate Professor at the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China.

Liang Xu is a Professor at the Institute of Artificial Intelligence, Shanghai University, Shanghai, China.

Qinglei Hu is a Professor at the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China.

Lihua Xie is a Professor at the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.

Table of Contents

Preface xv

Acknowledgments xvii

Acronyms xix

List of Symbols 1

1 Introduction 5

1.1 Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . 5

1.1.1 Networked Control Systems . . . . . . . . . . . . . . 5

1.1.2 Multi-Agent Systems . . . . . . . . . . . . . . . . . . 7

1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.1 Basics of Communication Theory . . . . . . . . . . . 9

1.2.2 Stabilization of NCSs . . . . . . . . . . . . . . . . . . 12

1.2.3 LQ Optimal Control of NCSs over Fading Channels 18

1.2.4 Estimation of NCSs with Intermittent Communication 20

1.2.5 Distributed Consensus of MASs . . . . . . . . . . . . 24

1.3 Preview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.4 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.4.1 Graph Theory . . . . . . . . . . . . . . . . . . . . . . 32

1.4.2 Hadamard Product and Kronecker Product . . . . . 33

vii

2 Stabilization over Power Constrained Fading Channels 53

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . 54

2.3 Fundamental Limitations . . . . . . . . . . . . . . . . . . . . . . 57

2.4 Mean-square Stabilizability . . . . . . . . . . . . . . . . . . . . . 62

2.4.1 Scalar Systems . . . . . . . . . . . . . . . . . . . . . . 64

2.4.2 Two-Dimensional Systems . . . . . . . . . . . . . . . 66

2.4.3 High-Dimensional Systems: TDMA Scheduler . . . 75

2.4.4 High-Dimensional Systems: Adaptive TDMA Scheduler

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.5 Numerical Illustrations . . . . . . . . . . . . . . . . . . . . . . . . 85

2.5.1 Scalar Systems . . . . . . . . . . . . . . . . . . . . . . 85

2.5.2 Vector Systems . . . . . . . . . . . . . . . . . . . . . 86

2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3 Stabilization over Gaussian Finite-State Markov Channels 93

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . 94

3.2.1 Stability of Markov Jump Linear Systems . . . . . . 97

3.2.2 Sojourn Times for Markov Lossy Process . . . . . . . 98

3.3 Fundamental Limitation . . . . . . . . . . . . . . . . . . . . . . . 99

3.4 Stabilization over Finite-state Markov channels . . . . . . . . . 104

3.4.1 Communication Structure . . . . . . . . . . . . . . . 105

3.4.2 Observer/Estimator/Controller Design . . . . . . . . 105

viii

3.4.3 Encoder/Decoder/Scheduler Design . . . . . . . . . 108

3.4.4 Sufficient Stabilizability Conditions . . . . . . . . . . 109

3.5 Stabilization over Markov Lossy Channels . . . . . . . . . . . . . 115

3.5.1 Two-dimensional Systems . . . . . . . . . . . . . . . 115

3.5.2 High-dimensional Systems . . . . . . . . . . . . . . . 123

3.5.3 Numerical Illustrations . . . . . . . . . . . . . . . . . 129

3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

4 Linear-Quadratic Optimal Control of NCSs with Random Input

Gains 135

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

4.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.3 Finite-horizon LQ Optimal Control . . . . . . . . . . . . . . . . . 141

4.4 Solvability of Modified Algebraic Riccati Equation . . . . . . . . 144

4.4.1 Cone-Invariant Operators . . . . . . . . . . . . . . . . 145

4.4.2 Solvability . . . . . . . . . . . . . . . . . . . . . . . . . 154

4.5 LQ Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . 173

4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

5 Multi-Sensor Kalman Filtering with Intermittent Measurements

189

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

5.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 190

5.3 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

5.3.1 Transmission Capacity . . . . . . . . . . . . . . . . . . 193

ix

5.3.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . 194

5.3.3 Lower Bound . . . . . . . . . . . . . . . . . . . . . . . 196

5.3.4 Upper Bound . . . . . . . . . . . . . . . . . . . . . . . 199

5.3.5 Special Cases . . . . . . . . . . . . . . . . . . . . . . . 211

5.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

6 Remote State Estimation with Stochastic Event-triggered Sensor

Schedule and Packet Drops 217

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

6.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 218

6.3 Optimal Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . 220

6.4 Sub-optimal Estimators . . . . . . . . . . . . . . . . . . . . . . . 229

6.4.1 Fixed Memory Estimator . . . . . . . . . . . . . . . . 229

6.4.2 Particle Filter . . . . . . . . . . . . . . . . . . . . . . . 232

6.5 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

7 Distributed Consensus over Undirected Fading Networks 245

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

7.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . 246

7.3 Identical Fading Networks . . . . . . . . . . . . . . . . . . . . . 248

7.4 Non-identical Fading Networks . . . . . . . . . . . . . . . . . . . 261

7.4.1 Definition of Edge Laplacian . . . . . . . . . . . . . . 261

7.4.2 Sufficient Consensus Conditions . . . . . . . . . . . . 263

x

7.5 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

8 Distributed Consensus over Directed Fading Networks 277

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

8.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . 278

8.3 Identical Fading Networks . . . . . . . . . . . . . . . . . . . . . 279

8.3.1 Consensus Error Dynamics . . . . . . . . . . . . . . . 280

8.3.2 Consensusability Results . . . . . . . . . . . . . . . . 283

8.3.3 Balanced Directed Graph Cases . . . . . . . . . . . . 286

8.4 Definitions and Properties of CIIM, CIM and CEL . . . . . . . 289

8.4.1 Definitions of CIIM, CIM and CEL . . . . . . . . . . 289

8.4.2 Properties of CIIM, CIM and CEL . . . . . . . . . . 292

8.5 Non-identical Fading Networks . . . . . . . . . . . . . . . . . . . 296

8.5.1 Λ = μI . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

8.5.2 Λ ̸= μI . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

8.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

8.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

9 Distributed Consensus over Networks with Communication

Delay and Packet Dropouts 315

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

9.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 316

9.3 Consensusability with Delay and Identical Packet Dropouts . . 318

xi

9.3.1 Stability Criterion of NCSs with Delay and Multiplicative

Noise . . . . . . . . . . . . . . . . . . . . . . 318

9.3.2 Consensusability Conditions . . . . . . . . . . . . . . 326

9.4 Consensusability with Delay and Non-Identical Packet Dropouts 334

9.5 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . 341

9.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

10 Distributed Consensus over Markovian Packet Loss Channels347

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

10.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . 348

10.3 Identical Markovian Packet Loss . . . . . . . . . . . . . . . . . . 349

10.3.1 Analytic Consensus Conditions . . . . . . . . . . . . . 355

10.3.2 Critical Consensus Condition for Scalar Agent Dynamics

. . . . . . . . . . . . . . . . . . . . . . . . . . . 358

10.4 Nonidentical Markovian Packet Loss . . . . . . . . . . . . . . . . 362

10.5 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . 367

10.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

11 Synchronization of the Delayed Vicsek Model 373

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

11.2 Directed Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

11.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 376

11.4 Synchronization of Delayed Linear Vicsek Model . . . . . . . . . 378

11.5 Synchronization of Delayed Nonlinear Vicsek Model . . . . . . . 386

11.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

11.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396