Matveev / Savkin Estimation and Control over Communication Networks

2009
ISBN: 978-0-8176-4607-3
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 533 Seiten

Reihe: Control Engineering

This book presents a systematic theory of estimation and control over communication networks. It develops a theory that utilizes communications, control, information and dynamical systems theory motivated and applied to advanced networking scenarios. The book establishes theoretically rich and practically important connections among modern control theory, Shannon information theory, and entropy theory of dynamical systems originated in the work of Kolmogorov. This self-contained monograph covers the latest achievements in the area. It contains many real-world applications and the presentation is accessible.

Autoren/Hrsg.

Matveev, Alexey S.

Savkin, Andrey V.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Introduction;16
3.1;1.1 Control Systems and Communication Networks;16
3.2;1.2 Overview of the Book;18
3.3;1.3 Frequently Used Notations;23
4;2 Topological Entropy, Observability, Robustness, Stabilizability, and Optimal Control;28
4.1;2.1 Introduction;28
4.2;2.2 Observability via Communication Channels;29
4.3;2.3 Topological Entropy and Observability of Uncertain Systems;30
4.4;2.4 The Case of Linear Systems;36
4.5;2.5 Stabilization via Communication Channels;39
4.6;2.6 Optimal Control via Communication Channels;41
4.7;2.7 Proofs of Lemma 2.4.3 and Theorems 2.5.3 and 2.6.4;43
5;3 Stabilization of Linear Multiple Sensor Systems via Limited Capacity Communication Channels;51
5.1;3.1 Introduction;51
5.2;3.2 Example;53
5.3;3.3 General Problem Statement;55
5.4;3.4 Basic Definitions and Assumptions;56
5.5;3.5 Main Result;65
5.6;3.6 Application of the Main Result to the Example from Sect. 3.2;71
5.7;3.7 Necessary Conditions for Stabilizability;73
5.8;3.8 Sufficient Conditions for Stabilizability;76
5.9;3.9 Comments on Assumption 3.4.24;104
6;4 Detectability and Output Feedback Stabilizability of Nonlinear Systems via Limited Capacity Communication Channels;115
6.1;4.1 Introduction;115
6.2;4.2 Detectability via Communication Channels;116
6.3;4.3 Stabilization via Communication Channels;122
6.4;4.4 Illustrative Example;125
7;5 Robust Set-Valued State Estimation via Limited Capacity Communication Channels;128
7.1;5.1 Introduction;128
7.2;5.2 Uncertain Systems;129
7.3;5.3 State Estimation Problem;132
7.4;5.4 Optimal Coder–Decoder Pair;135
7.5;5.5 Suboptimal Coder–Decoder Pair;136
7.6;5.6 Proofs of Lemmas 5.3.2 and 5.4.2;139
8;6 An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noiseless Plants via Noisy Discrete Channels;144
8.1;6.1 Introduction;144
8.2;6.2 State Estimation Problem;147
8.3;6.3 Assumptions, Notations, and Basic Definitions;149
8.4;6.4 Conditions for Observability of Noiseless Linear Plants;153
8.5;6.5 Stabilization Problem;156
8.6;6.6 Conditions for Stabilizability of Noiseless Linear Plants;158
8.7;6.7 Necessary Conditions for Observability and Stabilizability;160
8.8;6.8 Tracking with as Large a Probability as Desired: Proof of the c > H ( A ) . b) Part of Theorem 6.4.1;173
8.9;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;181
8.10;6.10 Completion of the Proof of Theorem 6.4.1 (on p. 140): Dropping Assumption 6.8.1 ( on p. 161);192
8.11;6.11 Stabilizing Controller and the Proof of the Sufficient Conditions for Stabilizability;192
9;7 An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noisy Plants via Noisy Discrete Channels;211
9.1;7.1 Introduction;211
9.2;7.2 Problem of State Estimation in the Face of System Noises;214
9.3;7.3 Zero Error Capacity of the Channel;215
9.4;7.4 Conditions for Almost Sure Observability of Noisy Plants;218
9.5;7.5 Almost Sure Stabilization in the Face of System Noises;220
9.6;7.6 Necessary Conditions for Observability and Stabilizability: Proofs of Theorem 7.4.1 and i) of Theorem 7.5.3;223
9.7;7.7 Almost Sure State Estimation in the Face of System Noises: Proof of Theorem 7.4.5;235
9.8;7.8 Almost Sure Stabilization in the Face of System Noises: Proof of ( ii) from Theorem 7.5.3;245
10;8 An Analog of Shannon Information Theory: Stable in Probability Control and State Estimation of Linear Noisy Plants via Noisy Discrete Channels;258
10.1;8.1 Introduction;258
10.2;8.2 Statement of the State Estimation Problem;260
10.3;8.3 Assumptions and Description of the Observability Domain;262
10.4;8.4 Coder–Decoder Pair Tracking the State in Probability;264
10.5;8.5 Statement of the Stabilization Problem;267
10.6;8.6 Stabilizability Domain;268
10.7;8.7 Stabilizing Coder–Decoder Pair;269
10.8;8.8 Proofs of Lemmas 8.2.4 and 8.5.3;275
11;9 Decentralized Stabilization of Linear Systems via Limited Capacity Communication Networks;280
11.1;9.1 Introduction;280
11.2;9.2 Examples Illustrating the Problem Statement;283
11.3;9.3 General Model of a Deterministic Network;293
11.4;9.4 Decentralized Networked Stabilization with Communication Constraints: The Problem Statement and Main Result;302
11.5;9.5 Examples and Some Properties of the Capacity Domain;312
11.6;9.6 Proof of the Necessity Part of Theorem 9.4.27;334
11.7;9.7 Proof of the Sufficiency Part of Theorem 9.4.27;341
11.8;9.8 Proofs of the Lemmas from Subsect. 9.5.2 and Remark 9.4.28;369
12;10 H8 State Estimation via Communication Channels;376
12.1;10.1 Introduction;376
12.2;10.2 Problem Statement;377
12.3;10.3 Linear State Estimator Design;378
13;11 Kalman State Estimation and Optimal Control Based on Asynchronously and Irregularly Delayed Measurements;381
13.1;11.1 Introduction;381
13.2;11.2 State Estimation Problem;382
13.3;11.3 State Estimator;384
13.4;11.4 Stability of the State Estimator;388
13.5;11.5 Finite Horizon Linear-Quadratic Gaussian Optimal Control Problem;391
13.6;11.6 Infinite Horizon Linear-Quadratic Gaussian Optimal Control Problem;392
13.7;11.7 Proofs of Theorems 11.3.3 and 11.5.1 and Remark 11.3.4;394
13.8;11.8 Proofs of the Propositions from Subsect. 11.4.1;397
13.9;11.9 Proof of Theorem 11.4.12 on p. 380;399
13.10;11.10 Proofs of Theorem 11.6.5 and Proposition 11.6.6 on p. 384;407
14;12 Optimal Computer Control via Asynchronous Communication Channels;415
14.1;12.1 Introduction;415
14.2;12.2 The Problem of Linear-Quadratic Optimal Control via Asynchronous Communication Channels;417
14.3;12.3 Optimal Control Strategy;421
14.4;12.4 Problem of Optimal Control of Multiple Semi-Independent Subsystems;425
14.5;12.5 Preliminary Discussion;428
14.6;12.6 Minimum Variance State Estimator;431
14.7;12.7 Solution of the Optimal Control Problem;434
14.8;12.8 Proofs of Theorem 12.3.3 and Remark 12.3.1;437
14.9;12.9 Proof of Theorem 12.6.2 on p. 424;445
14.10;12.10 Proofs of Theorem 12.7.1 and Proposition 12.7.2;448
15;13 Linear-Quadratic Gaussian Optimal Control via Limited Capacity Communication Channels;457
15.1;13.1 Introduction;457
15.2;13.2 Problem Statement;458
15.3;13.3 Preliminaries;459
15.4;13.4 Controller-Coder Separation Principle Does Not Hold;460
15.5;13.5 Solution of the Optimal Control Problem;463
15.6;13.6 Proofs of Lemma 13.5.3 and Theorems 13.4.2 and 13.5.2;466
15.7;13.7 Proof of Theorem 13.4.1;472
16;14 Kalman State Estimation in Networked Systems with Asynchronous Communication Channels and Switched Sensors;478
16.1;14.1 Introduction;478
16.2;14.2 Problem Statement;480
16.3;14.3 Assumptions;483
16.4;14.4 Minimum Variance State Estimator for a Given Sensor Control;485
16.5;14.5 Proof of Theorem 14.4.4;487
16.6;14.6 Optimal Sensor Control;491
16.7;14.7 Proof of Theorem 14.6.2 on p. 484;494
16.8;14.8 Model Predictive Sensor Control;496
17;15 Robust Kalman State Estimation with Switched Sensors;502
17.1;15.1 Introduction;502
17.2;15.2 Optimal Robust Sensor Scheduling;503
17.3;15.3 Model Predictive Sensor Scheduling;507
17.4;15.4 Proof of Theorems 15.2.13 and 15.3.3;509
18;Appendix A: Proof of Proposition 7.6.13 on p. 215;513
19;Appendix B: Some Properties of Square Ensembles of Matrices;515
20;Appendix C: Discrete Kalman Filter and Linear- Quadratic Gaussian Optimal Control Problem;517
21;Appendix D: Some Properties of the Joint Entropy of a Random Vector and Discrete Quantity;522
22;References;526
23;Index;538