Estimation and Control over Communication Networks (eBook)

Preface 6
Contents 8
1 Introduction 16
1.1 Control Systems and Communication Networks 16
1.2 Overview of the Book 18
1.3 Frequently Used Notations 23
2 Topological Entropy, Observability, Robustness, Stabilizability, and Optimal Control 28
2.1 Introduction 28
2.2 Observability via Communication Channels 29
2.3 Topological Entropy and Observability of Uncertain Systems 30
2.4 The Case of Linear Systems 36
2.5 Stabilization via Communication Channels 39
2.6 Optimal Control via Communication Channels 41
2.7 Proofs of Lemma 2.4.3 and Theorems 2.5.3 and 2.6.4 43
3 Stabilization of Linear Multiple Sensor Systems via Limited Capacity Communication Channels 51
3.1 Introduction 51
3.2 Example 53
3.3 General Problem Statement 55
3.4 Basic Definitions and Assumptions 56
3.5 Main Result 65
3.6 Application of the Main Result to the Example from Sect. 3.2 71
3.7 Necessary Conditions for Stabilizability 73
3.8 Sufficient Conditions for Stabilizability 76
3.9 Comments on Assumption 3.4.24 104
4 Detectability and Output Feedback Stabilizability of Nonlinear Systems via Limited Capacity Communication Channels 115
4.1 Introduction 115
4.2 Detectability via Communication Channels 116
4.3 Stabilization via Communication Channels 122
4.4 Illustrative Example 125
5 Robust Set-Valued State Estimation via Limited Capacity Communication Channels 128
5.1 Introduction 128
5.2 Uncertain Systems 129
5.3 State Estimation Problem 132
5.4 Optimal Coder–Decoder Pair 135
5.5 Suboptimal Coder–Decoder Pair 136
5.6 Proofs of Lemmas 5.3.2 and 5.4.2 139
6 An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noiseless Plants via Noisy Discrete Channels 144
6.1 Introduction 144
6.2 State Estimation Problem 147
6.3 Assumptions, Notations, and Basic Definitions 149
6.4 Conditions for Observability of Noiseless Linear Plants 153
6.5 Stabilization Problem 156
6.6 Conditions for Stabilizability of Noiseless Linear Plants 158
6.7 Necessary Conditions for Observability and Stabilizability 160
6.8 Tracking with as Large a Probability as Desired: Proof of the c > H ( A ) . b) Part of Theorem 6.4.1
6.9 Tracking Almost Surely by Means of Fixed-Length Code Words: Proof of the c > H ( A ) . a) part of Theorem 6.4.1
6.10 Completion of the Proof of Theorem 6.4.1 (on p. 140): Dropping Assumption 6.8.1 ( on p. 161) 192
6.11 Stabilizing Controller and the Proof of the Sufficient Conditions for Stabilizability 192
7 An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noisy Plants via Noisy Discrete Channels 211
7.1 Introduction 211
7.2 Problem of State Estimation in the Face of System Noises 214
7.3 Zero Error Capacity of the Channel 215
7.4 Conditions for Almost Sure Observability of Noisy Plants 218
7.5 Almost Sure Stabilization in the Face of System Noises 220
7.6 Necessary Conditions for Observability and Stabilizability: Proofs of Theorem 7.4.1 and i) of Theorem 7.5.3 223
7.7 Almost Sure State Estimation in the Face of System Noises: Proof of Theorem 7.4.5 235
7.8 Almost Sure Stabilization in the Face of System Noises: Proof of ( ii) from Theorem 7.5.3 245
8 An Analog of Shannon Information Theory: Stable in Probability Control and State Estimation of Linear Noisy Plants via Noisy Discrete Channels 258
8.1 Introduction 258
8.2 Statement of the State Estimation Problem 260
8.3 Assumptions and Description of the Observability Domain 262
8.4 Coder–Decoder Pair Tracking the State in Probability 264
8.5 Statement of the Stabilization Problem 267
8.6 Stabilizability Domain 268
8.7 Stabilizing Coder–Decoder Pair 269
8.8 Proofs of Lemmas 8.2.4 and 8.5.3 275
9 Decentralized Stabilization of Linear Systems via Limited Capacity Communication Networks 280
9.1 Introduction 280
9.2 Examples Illustrating the Problem Statement 283
9.3 General Model of a Deterministic Network 293
9.4 Decentralized Networked Stabilization with Communication Constraints: The Problem Statement and Main Result 302
9.5 Examples and Some Properties of the Capacity Domain 312
9.6 Proof of the Necessity Part of Theorem 9.4.27 334
9.7 Proof of the Sufficiency Part of Theorem 9.4.27 341
9.8 Proofs of the Lemmas from Subsect. 9.5.2 and Remark 9.4.28 369
10 H8 State Estimation via Communication Channels 376
10.1 Introduction 376
10.2 Problem Statement 377
10.3 Linear State Estimator Design 378
11 Kalman State Estimation and Optimal Control Based on Asynchronously and Irregularly Delayed Measurements 381
11.1 Introduction 381
11.2 State Estimation Problem 382
11.3 State Estimator 384
11.4 Stability of the State Estimator 388
11.5 Finite Horizon Linear-Quadratic Gaussian Optimal Control Problem 391
11.6 Infinite Horizon Linear-Quadratic Gaussian Optimal Control Problem 392
11.7 Proofs of Theorems 11.3.3 and 11.5.1 and Remark 11.3.4 394
11.8 Proofs of the Propositions from Subsect. 11.4.1 397
11.9 Proof of Theorem 11.4.12 on p. 380 399
11.10 Proofs of Theorem 11.6.5 and Proposition 11.6.6 on p. 384 407
12 Optimal Computer Control via Asynchronous Communication Channels 415
12.1 Introduction 415
12.2 The Problem of Linear-Quadratic Optimal Control via Asynchronous Communication Channels 417
12.3 Optimal Control Strategy 421
12.4 Problem of Optimal Control of Multiple Semi-Independent Subsystems 425
12.5 Preliminary Discussion 428
12.6 Minimum Variance State Estimator 431
12.7 Solution of the Optimal Control Problem 434
12.8 Proofs of Theorem 12.3.3 and Remark 12.3.1 437
12.9 Proof of Theorem 12.6.2 on p. 424 445
12.10 Proofs of Theorem 12.7.1 and Proposition 12.7.2 448
13 Linear-Quadratic Gaussian Optimal Control via Limited Capacity Communication Channels 457
13.1 Introduction 457
13.2 Problem Statement 458
13.3 Preliminaries 459
13.4 Controller-Coder Separation Principle Does Not Hold 460
13.5 Solution of the Optimal Control Problem 463
13.6 Proofs of Lemma 13.5.3 and Theorems 13.4.2 and 13.5.2 466
13.7 Proof of Theorem 13.4.1 472
14 Kalman State Estimation in Networked Systems with Asynchronous Communication Channels and Switched Sensors 478
14.1 Introduction 478
14.2 Problem Statement 480
14.3 Assumptions 483
14.4 Minimum Variance State Estimator for a Given Sensor Control 485
14.5 Proof of Theorem 14.4.4 487
14.6 Optimal Sensor Control 491
14.7 Proof of Theorem 14.6.2 on p. 484 494
14.8 Model Predictive Sensor Control 496
15 Robust Kalman State Estimation with Switched Sensors 502
15.1 Introduction 502
15.2 Optimal Robust Sensor Scheduling 503
15.3 Model Predictive Sensor Scheduling 507
15.4 Proof of Theorems 15.2.13 and 15.3.3 509
Appendix A: Proof of Proposition 7.6.13 on p. 215 513
Appendix B: Some Properties of Square Ensembles of Matrices 515
Appendix C: Discrete Kalman Filter and Linear- Quadratic Gaussian Optimal Control Problem 517
Appendix D: Some Properties of the Joint Entropy of a Random Vector and Discrete Quantity 522
References 526
Index 538