Estimation and Control of Large Scale Networked Systems is the first book that systematically summarizes results on large-scale networked systems. In addition, the book also summarizes the most recent results on structure identification of a networked system, attack identification and prevention. Readers will find the necessary mathematical knowledge for studying large-scale networked systems, as well as a systematic description of the current status of this field, the features of these systems, difficulties in dealing with state estimation and controller design, and major achievements.
Numerical examples in chapters provide strong application backgrounds and/or are abstracted from actual engineering problems, such as gene regulation networks and electricity power systems. This book is an ideal resource for researchers in the field of systems and control engineering.
Author(s): Tong Zhou, Keyou You, Tao Li
Publisher: B H
Year: 2018
Language: English
Pages: 484
Tags: Estimation ;Control; Large-Scale; Networked Systems
Front Matter......Page 2
Copyright......Page 5
Dedication......Page 6
Preface......Page 7
Acknowledgments......Page 9
Notation and Symbols......Page 10
1.1 A General View on Control System Design......Page 12
1.2 Communication and Control......Page 14
1.3 Book Contents......Page 17
1.3.1 Controllability and Observability of a Control System......Page 18
1.3.3 State Estimations and Control With Imperfect Communications......Page 19
1.3.5 Distributed Controller Design for an LSS......Page 20
1.3.7 Attack Estimation/Identification and Other Issues......Page 21
References......Page 22
2.1 Linear Space and Linear Algebra......Page 24
2.1.1 Vector and Matrix Norms......Page 31
2.1.2 Hamiltonian Matrices and Distance Among Positive Definite Matrices......Page 33
2.2 Generalized Inverse of a Matrix......Page 35
2.3 Some Useful Transformations......Page 37
2.4 Set Function and Submodularity......Page 40
2.5 Probability and Random Process......Page 43
2.6 Markov Process and Semi-Markov Process......Page 47
References......Page 50
3.1 Introduction......Page 52
3.2 Controllability and Observability of an LTI System......Page 53
3.2.1 Minimal Number of Inputs/Outputs Guaranteeing Controllability/Observability......Page 58
3.2.2 A Parameterization of Desirable Input/Output Matrices......Page 61
3.2.3 Some Nitpicking......Page 63
3.3 A General Model for an LSS......Page 64
3.4 Controllability and Observability for an LSS......Page 67
3.4.1 Subsystem Transmission Zeros and Observability of an LSS......Page 70
3.4.2 Observability Verification......Page 73
3.4.3 A Condition for Controllability and Its Verification......Page 75
3.4.4 In/Out-degree and Controllability/Observability of a Networked System......Page 77
3.5 Construction of Controllable/Observable Networked Systems......Page 83
3.6 Bibliographic Notes......Page 84
3.A.1 Proof of Theorem 3.4......Page 85
3.A.2 Proof of Theorem 3.8......Page 87
3.A.3 Proof of Theorem 3.9......Page 90
3.A.4 Proof of Theorem 3.10......Page 92
References......Page 94
4.2 State Estimation and Observer Design......Page 96
4.3 Kalman Filter as a Maximum Likelihood Estimator......Page 99
4.3.1 Derivation of the Kalman Filter......Page 101
4.3.2 Convergence Property of the Kalman Filter......Page 107
4.4.1 Estimation Algorithm......Page 109
4.4.2 Derivation of the Robust Estimator......Page 113
4.4.3 Asymptotic Properties of the Robust State Estimator......Page 118
4.4.4 Boundedness of Estimation Errors......Page 124
4.5 Bibliographic Notes......Page 126
4.A.1 Proof of Theorem 4.1......Page 127
4.A.2 Proof of Theorem 4.3......Page 129
References......Page 134
5.1 Introduction......Page 136
5.2 Intermittent Kalman Filtering (IKF)......Page 137
5.2.1 The IKF Algorithm......Page 138
5.2.2 Mean Square Stability of the IKF......Page 140
5.2.3 Weak Convergence of the IKF......Page 142
5.3 IKF With Switching Sensors......Page 143
5.3.1 Mean Square Stability......Page 146
5.3.2 Second-Order Systems......Page 152
5.3.3 Extension to Higher-Order Systems......Page 154
5.4.1 Linear Temporal Coding......Page 155
5.4.2 The MMSE Filter......Page 156
5.4.3 Mean Square Stability......Page 158
5.5.1 System With Parametric Errors......Page 162
5.5.2 Robust State Estimator......Page 163
5.5.3 Convergence of the Robust State Estimator......Page 165
5.6 Asymptotic Properties of State Estimations With Random Data Dropping......Page 167
5.6.1 Unified Problem Description and Preliminaries......Page 168
5.6.2 Asymptotic Properties of the Random Matrix Recursion......Page 169
5.6.3 Approximation of the Stationary Distribution......Page 174
5.A.1 Proof of Theorem 5.18......Page 179
5.A.2 Proof of Theorem 5.19......Page 183
5.A.4 Proof of Theorem 5.20......Page 187
5.A.5 Proof of Theorem 5.21......Page 189
5.A.6 Proof of Theorem 5.22......Page 192
References......Page 193
6.1 Introduction......Page 195
6.2 Predictor Design With Local Measurements......Page 196
6.2.1 Derivation of the Optimal Gain Matrix......Page 197
6.2.2 Relations With the Kalman Filter......Page 206
6.2.3 Robustification of the Distributed Predictor......Page 210
6.3 Distributed State Filtering......Page 214
6.4 Asymptotic Property of the Distributed Observers......Page 221
6.5 Distributed State Estimation Through Neighbor Information Exchanges......Page 223
6.A.1 Proof of Theorem 6.1......Page 229
6.A.2 Proof of Theorem 6.2......Page 232
6.A.3 Proof of Theorem 6.3......Page 234
6.A.4 Proof of Theorem 6.4......Page 236
6.A.5 Derivation of Eqs. (6.46) and (6.47)......Page 238
6.A.6 Proof of Theorem 6.7......Page 240
6.A.7 Proof of Theorem 6.8......Page 242
References......Page 244
7.1 Introduction......Page 246
7.2.1 System Description......Page 247
7.2.2 Stability of a Networked System......Page 248
7.2.3 Robust Stability of a Networked System......Page 257
7.3.1 Modeling Errors Described by IQCs......Page 259
7.3.2 Robust Stability With IQC-Described Modeling Errors......Page 261
7.5 Bibliographic Notes......Page 266
7.A.1 Proof of Theorem 7.3......Page 267
7.A.2 Proof of Theorem 7.4......Page 269
References......Page 272
8.1 Introduction......Page 274
8.2.1 Entropy in Information Theory......Page 275
8.2.2 Topological Entropy in Feedback Theory......Page 276
8.2.3 Channel Capacities......Page 277
8.3.1 Classical Approach for Quantized Control......Page 279
8.4 Universal Lower Bound......Page 281
8.5 Coder-Decoder Design......Page 282
8.6.1 Erasure Channels......Page 287
8.6.2 Gilbert-Elliott Channels......Page 288
8.7 Bibliographic Notes......Page 289
References......Page 290
9.1 Introduction......Page 292
9.2.1 Communication Graph......Page 293
9.3 Consensus Control With Relative State Feedback......Page 294
9.3.1 Design of Consensus Gain......Page 295
9.3.2 Extensions to Digraphs......Page 300
9.3.3 Performance Analysis......Page 303
9.3.4 Optimal Consensus Control for Second-Order Systems......Page 305
9.4.1 Distributed Observer-Based Protocol......Page 309
9.4.2 Consensus Under Static Protocol......Page 310
9.4.3 Consensus Under Dynamic Protocol......Page 312
9.4.4 Multiagent Systems With Double Integrators......Page 314
9.5 Formation Control for Multiagent Systems......Page 317
9.5.1 Vehicle Formation With Double Integrators......Page 318
9.5.2 Formation-Based Tracking Problem......Page 319
9.6.1 Modeling......Page 322
9.6.2 Simulation Results......Page 324
9.7 Bibliographic Notes......Page 326
References......Page 328
10.1 Introduction......Page 330
10.2 Steady-State Data-Based Identification......Page 332
10.2.1 Description of the Inference Procedure......Page 333
10.2.2 Identification Algorithm......Page 336
Position Determination for Direct Regulations......Page 337
Estimation of Regulation Coefficients......Page 342
Determination of the Number of Direct Regulations......Page 343
10.3 Absolute and Relative Variations in GRN Structure Estimations......Page 344
10.3.1 Maximum Likelihood Estimation for Wild-Type Expression Level and Measurement Error Variance......Page 346
10.3.2 Estimation of Relative Expression Level Variations......Page 349
10.3.3 Estimation Algorithm......Page 351
10.4 Estimation With Time Series Data......Page 352
10.4.1 Robust Structure Identification Algorithm for GRNs......Page 354
10.4.2 Convergence Analysis of the Robust Structure Identification Algorithm......Page 360
10.A.1 Proof of Theorem 10.4......Page 365
10.A.2 Proof of Theorem 10.5......Page 368
References......Page 371
11.1 Introduction......Page 375
11.2 The SCADA System......Page 378
11.3 Attack Prevention and System Transmission Zeros......Page 381
11.3.1 Zero Dynamics and Transmission Zeros......Page 385
11.3.2 Attack Prevention......Page 394
11.4 Detection of Attacks......Page 398
11.5 Identification of Attacks......Page 400
11.6 System Security and Sensor/Actuator Placement......Page 407
11.6.1 Some Properties of the Kalman Filter......Page 409
11.6.2 Sensor Placements......Page 413
11.6.3 Actuator Placements......Page 418
11.A.1 Proof of Theorem 11.7......Page 423
References......Page 426
12.1 Introduction......Page 428
12.2.1 Time Synchronization......Page 429
12.2.2 State Consensus......Page 431
Fixed Topology Case......Page 433
Time-Varying Topology Case......Page 444
Introduction......Page 452
Problem Formulation......Page 455
Control Design......Page 457
Closed-Loop Analysis......Page 460
12.4 Other Topics and Theoretical Challenges......Page 467
12.5 Bibliographic Notes......Page 470
12.A.1 Proof of Theorem 12.5......Page 471
References......Page 475
Index......Page 480
