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

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.

Table of Contents:
About the Authors xiii Preface xv Acknowledgments xvii Acronyms xix List of Symbols xxi 1 Introduction 1 1.1 Introduction and Motivation 1 1.1.1 Networked Control Systems 1 1.1.2 Multi-Agent Systems 2 1.2 Literature Review 4 1.2.1 Basics of Communication Theory 4 1.2.2 Stabilization of NCSs 6 1.2.2.1 Control over Noiseless Digital Channels 6 1.2.2.2 Control over Stochastic Digital Channels 7 1.2.2.3 Control over Analog Channels 8 1.2.3 LQ Optimal Control of NCSs over Fading Channels 9 1.2.4 Estimation of NCSs with Intermittent Communication 11 1.2.4.1 Stability of Kalman Filtering with Intermittent Observations 11 1.2.4.2 Remote State Estimation with Sensor Scheduling 12 1.2.5 Distributed Consensus of MASs 13 1.3 Preview of the Book 15 1.4 Preliminaries 18 1.4.1 Graph Theory 18 1.4.2 Hadamard Product and Kronecker Product 19 Bibliography 20 2 Stabilization over Power Constrained Fading Channels 29 2.1 Introduction 29 2.2 Problem Formulation 29 2.3 Fundamental Limitations 31 2.4 Mean-Square Stabilizability 35 2.4.1 Scalar Systems 36 2.4.2 Two-Dimensional Systems 37 2.4.2.1 Communication Structure 38 2.4.2.2 Encoder/Decoder Design 38 2.4.2.3 Scheduler Design 39 2.4.2.4 Scheduler Parameter Selection 40 2.4.2.5 Proof of Theorem 2.3 41 2.4.3 High-Dimensional Systems: TDMA Scheduler 44 2.4.4 High-Dimensional Systems: Adaptive TDMA Scheduler 45 2.4.4.1 Scheduling Algorithm 46 2.4.4.2 Scheduler Parameter Selection 46 2.4.4.3 Proof of Theorem 2.5 46 2.5 Numerical Illustrations 51 2.5.1 Scalar Systems 51 2.5.2 Vector Systems 52 2.6 Conclusions 53 Bibliography 53 3 Stabilization over Gaussian Finite-State Markov Channels 57 3.1 Introduction 57 3.2 Problem Formulation 58 3.2.1 Stability of Markov Jump Linear Systems 59 3.2.2 Sojourn Times for Markov Lossy Process 60 3.3 Fundamental Limitation 61 3.4 Stabilization over Finite-State Markov Channels 64 3.4.1 Communication Structure 65 3.4.2 Observer/Estimator/Controller Design 65 3.4.3 Encoder/Decoder/Scheduler Design 67 3.4.4 Sufficient Stabilizability Conditions 68 3.5 Stabilization over Markov Lossy Channels 71 3.5.1 Two-Dimensional Systems 71 3.5.1.1 Optimal Scheduler Design 72 3.5.1.2 Scheduler Parameter Selection 74 3.5.1.3 Sufficiency Proof of Theorem 3.4 75 3.5.2 High-Dimensional Systems 77 3.5.3 Numerical Illustrations 81 3.6 Conclusions 82 Bibliography 83 4 Linear-Quadratic Optimal Control of NCSs with Random Input Gains 85 4.1 Introduction 85 4.2 Problem Formulation 86 4.3 Finite-Horizon LQ Optimal Control 88 4.4 Solvability of Modified Algebraic Riccati Equation 91 4.4.1 Cone-Invariant Operators 91 4.4.2 Solvability 97 4.5 LQ Optimal Control 108 4.6 Conclusion 114 Bibliography 115 5 Multisensor Kalman Filtering with Intermittent Measurements 117 5.1 Introduction 117 5.2 Problem Formulation 118 5.3 Stability Analysis 120 5.3.1 Transmission Capacity 120 5.3.2 Preliminaries 120 5.3.3 Lower Bound 121 5.3.4 Upper Bound 124 5.3.5 Special Cases 130 5.4 Examples 131 5.5 Conclusions 132 Bibliography 133 6 Remote State Estimation with Stochastic Event-Triggered Sensor Schedule and Packet Drops 135 6.1 Introduction 135 6.2 Problem Formulation 135 6.3 Optimal Estimator 137 6.4 Suboptimal Estimators 143 6.4.1 Fixed Memory Estimator 143 6.4.2 Particle Filter 145 6.5 Simulations 149 6.6 Conclusions 151 Bibliography 152 7 Distributed Consensus over Undirected Fading Networks 153 7.1 Introduction 153 7.2 Problem Formulation 154 7.3 Identical Fading Networks 155 7.4 Nonidentical Fading Networks 163 7.4.1 Definition of Edge Laplacian 163 7.4.2 Sufficient Consensus Conditions 164 7.5 Simulations 168 7.6 Conclusions 170 Bibliography 170 8 Distributed Consensus over Directed Fading Networks 173 8.1 Introduction 173 8.2 Problem Formulation 174 8.3 Identical Fading Networks 174 8.3.1 Consensus Error Dynamics 175 8.3.2 Consensusability Results 177 8.3.3 Balanced Directed Graph Cases 179 8.4 Definitions and Properties of CIIM, CIM, and CEL 181 8.4.1 Definitions of CIIM, CIM, and CEL 181 8.4.2 Properties of CIIM, CIM, and CEL 182 8.5 Nonidentical Fading Networks 185 8.5.1 Λ=μI 189 8.5.1.1 Star Graphs 190 8.5.1.2 Directed Path Graphs 191 8.5.2 Λ ≠ μI 192 8.6 Simulations 192 8.7 Conclusions 194 Bibliography 195 9 Distributed Consensus over Networks with Communication Delay and Packet Dropouts 197 9.1 Introduction 197 9.2 Problem Formulation 198 9.3 Consensusability with Delay and Identical Packet Dropouts 199 9.3.1 Stability Criterion of NCSs with Delay and Multiplicative Noise 199 9.3.2 Consensusability Conditions 204 9.4 Consensusability with Delay and Nonidentical Packet Dropouts 209 9.5 Illustrative Examples 214 9.6 Conclusions 216 Bibliography 216 10 Distributed Consensus over Markovian Packet Loss Channels 219 10.1 Introduction 219 10.2 Problem Formulation 219 10.3 Identical Markovian Packet Loss 220 10.3.1 Analytic Consensus Conditions 224 10.3.2 Critical Consensus Condition for Scalar Agent Dynamics 226 10.4 Nonidentical Markovian Packet Loss 228 10.5 Numerical Simulations 232 10.6 Conclusions 234 Bibliography 235 11 Synchronization of the Delayed Vicsek Model 237 11.1 Introduction 237 11.2 Directed Graphs 238 11.3 Problem Formulation 239 11.4 Synchronization of Delayed Linear Vicsek Model 240 11.5 Synchronization of Delayed Nonlinear Vicsek Model 246 11.6 Simulations 249 11.7 Conclusions 253 Bibliography 253 Index 255