Control Theory of Digitally Networked Dynamic Systems (eBook)

Preface 5
Contents 8
List of Contributors 9
Notation 14
Introduction to Networked Control Systems 15
1.1 What Are Networked Control Systems? 16
1.1.1 Motivation and Examples 16
1.1.2 Cyber-Physical Systems 20
1.1.3 Structures of Networked Control Systems 22
1.2 Theory of Networked Control Systems 24
1.2.1 Overview 24
1.2.2 Control with Information Rate Constraints 26
1.2.3 Control Subject to Networked-Induced Time Delays 27
1.2.4 Control Subject to Packet Loss 30
1.2.5 Control under Restrictions on the Network Access 31
1.2.6 Distributed Control of Interconnected Systems and Multi-Agent Systems 36
1.3 New Mathematical Concepts for Networked Control Systems 41
1.3.1 Optimization and Optimal Control 41
1.3.2 Dynamical Properties of Control Systems: Controllability,Observability and Stability 42
1.3.3 Graph Theory and Structured Matrices 44
Analysis of Networked Systems 45
2.1 Overview 46
2.2 Observability of Networked Systems 48
2.2.1 Motivation and Earlier Results 48
2.2.2 Reachability and Observability of Networks 50
2.2.3 Sensitivity Analysis of Networks 61
2.3 Minimal Bit Rates and Entropy for Control Tasks 66
2.3.1 Motivation and Earlier Results 66
2.3.2 Invariance Entropy 67
2.3.3 Entropy for Exponential Stabilization 76
2.4 Dynamic Quantization for Feedback Stabilization with Delayed Data-Rate Limited Communication 83
2.4.1 Problem Statement 83
2.4.2 Dynamic Quantization 83
2.4.3 Markovian Communication Models 90
Distributed Estimation and Control 94
3.1 Estimation and Control Architectures 95
3.1.1 Distribution of Control Tasks 95
3.1.2 Distributed Control Design 97
3.1.3 Contributions of this Book to Distributed Control 98
3.2 Centralized and Decentralized Moving-Horizon Estimation for Networked Control Systems 99
3.2.1 Centralized and Decentralized Networked Control Architecture 99
3.2.2 Problem Formulation 101
3.2.3 Centralized Moving-Horizon Estimation 102
3.2.4 Decentralized Moving-Horizon Estimation 105
3.3 Towards a Two-Layer Optimal ControlArchitecture for Distributed Systems 113
3.3.1 Distributed Optimization 113
3.3.2 Control of Distributed Systems 116
3.3.3 Dual Decomposition of the DC Optimal Power FlowProblem 119
3.3.4 Distributed Controller Design with Local ModelInformation 121
Distributed and Networked Model Predictive Control 124
4.1 Model Predictive Control of Networked Systems 126
4.1.1 Chapter Overview 126
4.1.2 Distributed and Decentralized Systems 127
4.1.3 Brief Review of Model Predictive Control (MPC) 127
4.2 Compensation of Delays and Packet Loss 131
4.2.1 Problem Setup 132
4.2.2 Model-Based Compensation of Network Effects 133
4.2.3 Stability Properties of Model-Based Compensation 135
4.2.4 Outlook to Time-Delay Systems 138
4.3 Decentralized and Distributed Control Algorithms 139
4.3.1 Dissipativity-Based Distributed MPC 140
4.3.2 Decentralized MPC without Terminal Constraints 144
4.3.3 Distributed MPC for Cooperative Control 148
4.4 Distributed Predictive Control of Communicating Decentralized Systems 152
4.4.1 Survey of Distributed MPC 152
4.4.2 A Set-Invariance Approach to Distributed MPC 156
4.4.3 Distributed MPC Based on Robust Optimization 157
4.4.4 Distributed MPC for Hybrid Systems 166
4.5 Stochastic Model-Based Control with Virtual Control Inputs 169
4.5.1 System Setup and Controller-Actuator Scheme 170
4.5.2 Concept of Virtual Control Inputs 173
4.5.3 Model Predictive Controller Design Using Virtual Control Inputs 177
4.5.4 Model-Based Extension of Feedback Controllers Using Virtual Control Inputs 178
Event-Based Control 181
5.1 Introduction to Event-Based Control 183
5.2 Disturbance Attenuation by Event-Based State Feedback 187
5.2.1 Control Aim 187
5.2.2 Continuous State Feedback 188
5.2.3 Event-Based State Feedback 190
5.2.4 Main Properties of the Event-Based State-Feedback Loop 195
5.2.5 Extensions 198
5.3 Event-Based Stabilization of Interconnected Systems 203
5.3.1 Control of Interconnected Systems 203
5.3.2 Distributed Realization of the Event-Based State Feedback 204
5.3.3 Decentralized Event-Based State Feedback 207
5.4 Optimization-Based Control 215
5.4.1 Problem Formulation 216
5.4.2 Optimality Principle 216
5.4.3 Discretization of the State Space 217
5.4.4 Dynamic Games 219
5.4.5 Discretization as Perturbation 222
5.4.6 Event-Based Implementation 223
5.4.7 Including Past Information 225
5.4.8 Including Network Effects 226
5.4.9 Construction of a Lazy Feedback 229
5.4.10 Combination of the Global and the Local Approach 231
5.5 A Small-Gain Perspective on Event-Based Control 232
5.5.1 Problem Statement 232
5.5.2 Event Generation and Input-to-State Stability 234
5.5.3 Practical Stabilization 240
5.5.4 Parsimonious Triggering and Asymptotic Stabilization 241
5.5.5 Comparison of the Different Approaches 244
5.6 Event-Based Control of Interconnected Nonlinear Systems 246
5.6.1 Problem Statement 246
5.6.2 ISS-Based Decentralized Feedback Design 247
5.6.3 Optimization-Based Centralized Feedback Design 251
5.7 A Stochastic Approach to Event-Based Control 257
5.7.1 Event-Based Control as a Two-Person Team Problem 257
5.7.2 Problem Formulation 258
5.7.3 Optimal Time-Triggered Transmission 260
5.7.4 Optimal Event-Triggered Transmission 263
5.8 Appendix: The Thermofluid Process used for Experiments 269
Multi-agent Systems 274
6.1 Control Problems for Multi-agent Systems 276
6.2 Synchronization of Agents with Individual Dynamics 279
6.2.1 Synchronization Problem 279
6.2.2 Models 282
6.2.3 Internal-Reference Principle 284
6.2.4 Asymptotic Synchronization 286
6.2.5 Controller Design for Synchronization 292
6.3 Synchronizing Subspaces and Geometric Control 294
6.3.1 Motivation and Earlier Results 294
6.3.2 Stability and Stabilization of Homogenous Networks 296
6.3.3 Synchronization of Homogenous Networks 301
6.4 Optimization Methods for Cluster Synchronization Analysis 305
6.4.1 Cluster Synchronization 305
6.4.2 A Dynamic Network Model for Clustering 306
6.4.3 Combinatorial Conditions for Synchronization 309
6.4.4 Static Saddle-Point Problem for Clustering Analysis 311
6.4.5 Hierarchical Clustering Analysis and Community Detection 314
6.5 Autonomy and Cooperation in Networked Systems 316
6.5.1 Information Reduction in the Control of Systems with Identical Subsystems 316
6.5.2 System Models 318
6.5.3 Offline Information Reduction: Decomposition of the Controller Design Problem 319
6.5.4 Online Information Reduction: Situation-Dependent Communication 325
6.5.5 Stability Analysis of Subsystems with Similar Dynamics 329
Wireless Networking for Control 336
7.1 Control Implications of Wireless Networks 337
7.2 Control and Communication Co-design 339
7.2.1 Cross-Layering 339
7.2.2 Control Design 343
7.2.3 Communication Design 353
7.3 Control Requirements on Network Protocols 360
7.3.1 Load, Loss and Control Performance 360
7.3.2 Control Problem (Application Layer) 361
7.3.3 Comparison of Event-Based and Time-Triggered Control 363
7.3.4 Properties of Communication Systems (MAC Layer) 365
7.3.5 Control Performance for Different CommunicationSchemes 370
References 374
Index 397