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Estimation and Control over Communication Networks 2009 ed. [Hardback]

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  • Formāts: Hardback, 533 pages, height x width: 235x155 mm, weight: 986 g, 95 Illustrations, black and white; XIV, 533 p. 95 illus., 1 Hardback
  • Sērija : Control Engineering
  • Izdošanas datums: 08-Oct-2008
  • Izdevniecība: Birkhauser Boston Inc
  • ISBN-10: 0817644946
  • ISBN-13: 9780817644949
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Estimation and Control over Communication Networks 2009 ed.Palielināt
  • Formāts: Hardback, 533 pages, height x width: 235x155 mm, weight: 986 g, 95 Illustrations, black and white; XIV, 533 p. 95 illus., 1 Hardback
  • Sērija : Control Engineering
  • Izdošanas datums: 08-Oct-2008
  • Izdevniecība: Birkhauser Boston Inc
  • ISBN-10: 0817644946
  • ISBN-13: 9780817644949
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780817644949.html
Keywords:
Although there is an emerging literature on the topic, this is the first book that attempts to present a systematic theory of estimation and control over communication networks. Using several selected problems of estimation and control over communication networks, the authors present and prove a number of results concerning optimality, stability, and robustness having practical significance for networked control system design. In particular, various problems of Kalman filtering, stabilization, and optimal control over communication channels are considered and solved. The results establish fundamental links among mathematical control theory, Shannon information theory, and entropy theory of dynamical systems.



This essentially self-contained monograph offers accessible mathematical models and results for advanced postgraduate students, researchers, and practitioners working in the areas of control engineering, communications, information theory, signal processing, and applied mathematics.

Recenzijas

From the reviews:

"The first book that attempts to presents a systematic theory of estimation and control over communication networks. The book is an excellent up-to-date resource of working knowledge with long-term evidence in the field. The text can serve also as a useful reference book about this challenging research topic. The monograph is intended for researchers, practitioners, postgraduate students, and all professionals interested in the emerging subject of networked control systems." (Lubomķr Bakule, Zentralblatt MATH, Vol. 1165, 2009)

This book is a research monograph that is concerned with problems of control and state estimation over communication networks. The book begins with an introduction that outlines the main problems that will be addressed in the book. Overall, the book presents a range of new results in the area of control and state estimation via communication networks.­­­ (Ian Petersen, Mathematical Reviews, Issue 2010 g)

Preface
1 Introduction
1
1.1 Control Systems and Communication Networks
1
1.2 Overview of the Book
3
1.2.1 Estimation and Control over Limited Capacity Deterministic Channels
3
1.2.2 An Analog of Shannon Information Theory: Estimation and Control over Noisy Discrete Channels
5
1.2.3 Decentralized Stabilization via Limited Capacity Communication Networks
6
1.2.4 Hinfinity State Estimation via Communication Channels
6
1.2.5 Kalman Filtering and Optimal Control via Asynchronous Channels with Irregular Delays
7
1.2.6 Kalman. Filtering with Switched Sensors
7
1.2.7 Some Other Remarks
8
1.3 Frequently Used Notations
8
2 Topological Entropy, Observability, Robustness, Stabilizability, and Optimal Control
13
2.1 Introduction
13
2.2 Observability via Communication Channels
14
2.3 Topological Entropy and Observability of Uncertain Systems
15
2.4 The Case of Linear Systems
21
2.5 Stabilization via Communication Channels
24
2.6 Optimal Control via Communication Channels
26
2.7 Proofs of Lemma 2.4.3 and Theorems 2.5.3 and 2.6.4
28
3 Stabilization of Linear Multiple Sensor Systems via Limited Capacity Communication Channels
37
3.1 Introduction
37
3.2 Example
39
3.3 General Problem Statement
41
3.4 Basic Definitions and Assumptions
42
3.4.1 Transmission Capacity of the Channel
42
3.4.2 Examples
44
3.4.3 Stabilizable Multiple Sensor Systems
45
3.4.4 Recursive Semirational Controllers
46
3.4.5 Assumptions about the System (3.3.1), (3.3.2)
49
3.5 Main Result
51
3.5.1 Some Consequences from the Main Result
55
3.5.2 Complement to the Sufficient Conditions
55
3.5.3 Complements to the Necessary Conditions
56
3.6 Application of the Main Result to the Example from Sect. 3.2
57
3.7 Necessary Conditions for Stabilizability
59
3.7.1 An Extension of the Claim (i) from Theorem 2.5.3 (on p. 26)
59
3.7.2 An Auxiliary Subsystem
60
3.7.3 Stabilizability of the Auxiliary Subsystem
61
3.7.4 Proof of the Necessity Part (i) (ii) of Theorem 3.5.2
62
3.8 Sufficient Conditions for Stabilizability
62
3.8.1 Some Ideas Underlying the Design of the Stabilizing Controller
63
3.8.2 Plan of Proving the Sufficiency Part of Theorem 3.5.2
65
3.8.3 Decomposition of the System
66
3.8.4 Separate Stabilization of Subsystems
68
3.8.5 Contracted Quantizer with the Nearly Minimal Number of Levels
77
3.8.6 Construction of a Deadbeat Stabilizer
80
3.8.7 Stabilization of the Entire System
81
3.8.8 Analysis of Assumptions Al) and A2) on p. 81
83
3.8.9 Inconstructive Sufficient Conditions for Stabilizability
85
3.8.10 Convex Duality and a Criterion for the System (3.8.34) to be Solvable
86
3.8.11 Proof of the Sufficiency Part of Theorem 3.5.2 for Systems with Both Unstable and Stable Modes
88
3.8.12 Completion of the Proof of Theorem 3.5.2 and the Proofs of Propositions 3.5.4 and 3.5.8
89
3.9 Comments on Assumption 3.4.24
90
3.9.1 Counterexample
91
3.9.2 Stabilizability of the System (3.9.2)
93
4 Detectability and Output Feedback Stabilizability of Nonlinear Systems via Limited Capacity Communication Channels
101
4.1 Introduction
101
4.2 Detectability via Communication Channels
102
4.2.1 Preliminary Lemmas
103
4.2.2 Uniform State Quantization
105
4.3 Stabilization via Communication Channels
108
4.4 Illustrative Example
111
5 Robust Set-Valued State Estimation via Limited Capacity Communication Channels
115
5.1 Introduction
115
5.2 Uncertain Systems
116
5.2.1 Uncertain Systems with Integral Quadratic Constraints
116
5.2.2 Uncertain Systems with Norm-Bounded Uncertainty
117
5.2.3 Sector-Bounded Nonlinearities
118
5.3 State Estimation Problem
119
5.4 Optimal Coder–Decoder Pair
122
5.5 Suboptimal Coder–Decoder Pair
123
5.6 Proofs of Lemmas 5.3.2 and 5.4.2
126
6 An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noiseless Plants via Noisy Discrete Channels
131
6.1 Introduction
131
6.2 State Estimation Problem
134
6.3 Assumptions, Notations, and Basic Definitions
136
6.3.1 Assumptions
136
6.3.2 Average Mutual Information
137
6.3.3 Capacity of a Discrete Memoryless Channel
138
6.3.4 Recursive Semirational Observers
139
6.4 Conditions for Observability of Noiseless Linear Plants
140
6.5 Stabilization Problem
143
6.6 Conditions for Stabilizability of Noiseless Linear Plants
145
6.6.1 The Domain of Stabilizability Is Determined by the Shannon Channel Capacity
145
6.7 Necessary Conditions for Observability and Stabilizability
147
6.7.1 Proposition 6.7.2 Follows from Proposition 6.7.1
148
6.7.2 Relationship between the Statements (i) and (ii) of Proposition 6.7 1
149
6.7.3 Differential Entropy of a Random Vector and Joint Entropy of a Random Vector and Discrete Quantity
150
6.7.4 Probability of Large Estimation Errors
152
6.7.5 Proof of Proposition 6.7.1 under Assumption 6.7.11
155
6.7.6 Completion of the Proofs of Propositions 6.7.1 and 6.7.2: Dropping Assumption 6.7.11
156
6.8 Tracking with as Large a Probability as Desired: Proof of the c greater than H(A) b) Part of Theorem 6.4 1
160
6.8.1 Error Exponents for Discrete Memoryless Channels
161
6.8.2 Coder–Decoder Pair without a Communication Feedback
162
6.8.3 Tracking with as Large a Probability as Desired without a Communication Feedback
165
6.9 Tracking Almost Surely by Means of Fixed-Length Code Words: Proof of the c greater than H (A) a) part of Theorem 6.4.1
168
6.9.1 Coder–Decoder Pair with a Communication Feedback
168
6.9.2 Tracking Almost Surely by Means of Fixed-Length Code Words
170
6.9.3 Proof of Proposition 6.9.8
171
6.10 Completion of the Proof of Theorem 6.4.1 (on p. 140): Dropping Assumption 6.8.1 (on p. 161)
179
6.11 Stabilizing Controller and the Proof of the Sufficient Conditions for Stabilizability
179
6.11.1 Almost Sure Stabilization by Means of Fixed-Length Code Words and Low-Rate Feedback Communication
180
6.11.2 Almost Sure Stabilization by Means of Fixed-Length Code Words in the Absence of a Special Feedback Communication Link
185
6.11.3 Proof of Proposition 6.11.22
188
6.11.4 Completion of the Proof of Theorem 6.6.1
196
7 An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noisy Plants via Noisy Discrete Channels
199
7.1 Introduction
199
7.2 Problem of State Estimation in the Face of System Noises
202
7.3 Zero Error Capacity of the Channel
203
7.4 Conditions for Almost Sure Observability of Noisy Plants
206
7.5 Almost Sure Stabilization in the Face of System Noises
208
7.6 Necessary Conditions for Observability and Stabilizability: Proofs of Theorem 7.4.1 and i) of Theorem 7.5.3
211
7.6.1 Proof of i) in Proposition 7.6.2 for Erasure Channels
211
7.6.2 Preliminaries
214
7.6.3 Block Codes Fabricated from the Observer
218
7.6.4 Errorless Block Code Hidden within a Tracking Observer
220
7.6.5 Completion of the Proofs of Proposition 7.6.2, 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
223
7.7.1 Construction of the Coder and Decoder-Estimator
223
7.7.2 Almost Sure State Estimation in the Face of System Noises
227
7.7.3 Completion of the Proof of Theorem 7.4.5
232
7.8 Almost Sure Stabilization in the Face of System Noises: Proof of (ii) from Theorem 7.5.3
233
7.8.1 Feedback Information Transmission by Means of Control
233
7.8.2 Zero Error Capacity with Delayed Feedback
235
7.8.3 Construction of the Stabilizing Coder and Decoder-Controller
236
7.8.4 Almost Sure Stabilization in the Face of Plant Noises
241
7.8.5 Completion of the Proof of (ii) from Theorem 7.5.3
244
8 An Analog of Shannon Information Theory: Stable in Probability Control and State Estimation of Linear Noisy Plants via Noisy Discrete Channels
247
8.1 Introduction
247
8.2 Statement of the State Estimation Problem
249
8.3 Assumptions and Description of the Observability Domain
251
8.4 Coder–Decoder Pair Tracking the State in Probability
253
8.5 Statement of the Stabilization Problem
256
8.6 Stabilizability Domain
257
8.7 Stabilizing Coder–Decoder Pair
258
8.7.1 Stabilizing Coder–Decoder Pair without a Communication Feedback
258
8.7.2 Universal Stabilizing Coder–Decoder Pair Consuming Feedback Communication of an Arbitrarily Low Rate
262
8.7.3 Proof of Lemma 8.7.1
263
8.8 Proofs of Lemmas 8.2.4 and 8.5 3
264
9 Decentralized Stabilization of Linear Systems via Limited Capacity Communication Networks
269
9.1 Introduction
269
9.2 Examples Illustrating the Problem Statement
272
9.3 General Model of a Deterministic Network
282
9.3.1 How the General Model Arises from a Particular Example of a Network
282
9.3.2 Equations (9.3.2) for the Considered Example
284
9.3.3 General Model of the Communication Network
285
9.3.4 Concluding Remarks
288
9.4 Decentralized Networked Stabilization with Communication Constraints: The Problem Statement and Main Result
291
9.4.1 Statement of the Stabilization Problem
291
9.4.2 Control-Based Extension of the Network
293
9.4.3 Assumptions about the Plant
294
9.4.4 Mode-Wise Prefix
295
9.4.5 Mode-Wise Suffix and the Final Extended Network
296
9.4.6 Network Capacity Domain
297
9.4.7 Final Assumptions about the Network
298
9.4.8 Criterion for Stabilizability
300
9.5 Examples and Some Properties of the Capacity Domain
301
9.5.1 Capacity Domain of Networks with Not Necessarily Equal Numbers of Data Sources and Outputs
301
9.5.2 Estimates of the Capacity Domain from Theorem 9.4.27 and Relevant Facts
304
9.5.3 Example 1: Platoon of Independent Agents
308
9.5.4 Example 2: Plant with Two Sensors and Actuators
310
9.6 Proof of the Necessity Part of Theorem 9.4.27
323
9.6.1 Plan on the Proof
324
9.6.2 Step 1: Network Converting the Initial State into the Controls
325
9.6.3 Step 2: Networked Estimator of the Open-Loop Plant Modes
326
9.6.4 Step 3: Completion of the Proof of c) d) Part of Theorem 9.4.27
329
9.7 Proof of the Sufficiency Part of Theorem 9.4.27
330
9.7.1 Synchronized Quantization of Signals from Independent Noisy Sensors
330
9.7.2 Master for Sensors Observing a Given Unstable Mode
333
9.7.3 Stabilization over the Control-Based Extension of the Original Network
336
9.7.4 Completing the Proof of b) from Theorem 9.4.27: Stabilization over the Original Network
348
9.8 Proofs of the Lemmas from Subsect. 9.5.2 and Remark 9.4.28
358
9.8.1 Proof of Lemma 9.5.6 on p. 303
358
9.8.2 Proof of Lemma 9.5.8 on p. 304
360
9.8.3 Proof of Lemma 9.5.10 on p. 306
360
9.8.4 Proof of Remark 9.4.28 on p. 300
362
10 Hinfinity State Estimation via Communication Channels 365
10.1 Introduction
365
10.2 Problem Statement
366
10.3 Linear State Estimator Design
367
11 Kalman State Estimation and Optimal Control Based on Asynchronously and Irregularly Delayed Measurements 371
11.1 Introduction
371
11.2 State Estimation Problem
372
11.3 State Estimator
374
11.3.1 Pseudoinverse of a Square Matrix and Ensemble of Matrices
374
11.3.2 Description of the State Estimator
375
11.3.3 The Major Properties of the State Estimator
377
11.4 Stability of the State Estimator
378
11.4.1 Almost Sure Observability via the Communication Channels
378
11.4.2 Conditions for Stability of the State Estimator
380
11.5 Finite Horizon Linear-Quadratic Gaussian Optimal Control Problem
381
11.6 Infinite Horizon Linear-Quadratic Gaussian Optimal Control Problem
382
11.7 Proofs of Theorems 11.3.3 and 11.5.1 and Remark 11.3.4
384
11.8 Proofs of the Propositions from Subsect. 11.4.1
387
11.9 Proof of Theorem 11.4.12 on p. 380
389
11.10 Proofs of Theorem 11.6.5 and Proposition 11.6.6 on p. 384
397
12 Optimal Computer Control via Asynchronous Communication Channels 405
12.1 Introduction
405
12.2 The Problem of Linear-Quadratic Optimal Control via Asynchronous Communication Channels
407
12.2.1 Problem Statement
407
12.2.2 Assumptions
409
12.3 Optimal Control Strategy
411
12.4 Problem of Optimal Control of Multiple Semi-Independent Subsystems
415
12.4.1 Problem Statement
415
12.4.2 Assumptions
417
12.5 Preliminary Discussion
418
12.6 Minimum Variance State Estimator
421
12.7 Solution of the Optimal Control Problem
424
12.8 Proofs of Theorem 12.3.3 and Remark 12.3.1
427
12.9 Proof of Theorem 12.6.2 on p. 424
435
12.10 Proofs of Theorem 12.7.1 and Proposition 12.7.2
438
12.10.1 Preliminaries
438
12.10.2 Proof of Theorem 12.7.1 on p. 426: Single Subsystem
440
12.10.3 Proofs of Theorem 12.7.1 and Proposition 12.7.2: Many Subsystems
443
13 Linear-Quadratic Gaussian Optimal Control via Limited Capacity Communication Channels 447
13.1 Introduction
447
13.2 Problem Statement
448
13.3 Preliminaries
449
13.4 Controller-Coder Separation Principle Does Not Hold
450
13.5 Solution of the Optimal Control Problem
453
13.6 Proofs of Lemma 13.5.3 and Theorems 13.4.2 and 13.5.2
456
13.7 Proof of Theorem 13.4.1
462
14 Kalman State Estimation in Networked Systems with Asynchronous Communication Channels and Switched Sensors 469
14.1 Introduction
469
14.2 Problem Statement
471
14.3 Assumptions
474
14.3.1 Properties of the Sensors and the Process
474
14.3.2 Information about the Past States of the Communication Network
475
14.3.3 Properties of the Communication Network
475
14.4 Minimum Variance State Estimator for a Given Sensor Control
476
14.5 Proof of Theorem 14.4.4
478
14.6 Optimal Sensor Control
482
14.7 Proof of Theorem 14.6.2 on p. 484
485
14.8 Model Predictive Sensor Control
487
15 Robust Kalman State Estimation with Switched Sensors 493
15.1 Introduction
493
15.2 Optimal Robust Sensor Scheduling
494
15.3 Model Predictive Sensor Scheduling
498
15.4 Proof of Theorems 15.2.13 and 15.3.3
500
Appendix A: Proof of Proposition 7.6.13 505
Appendix B: Some Properties of Square Ensembles of Matrices
507
Appendix C: Discrete Kalman Filter and Linear-Quadratic Gaussian Optimal Control Problem
509
C.1 Problem Statement
509
C.2 Solution of the State Estimation Problem: The Kalman Filter
510
C.3 Solution of the LOG Optimal Control Problem
512
Appendix D: Some Properties of the Joint Entropy of a Random Vector andDiscrete Quantity
515
D.1 Preliminary technical fact
515
D.2 Proof of (6.7.14) on p. 151
517
D.3 Proof of (6.7.12) on p. 151
517
References 519
Index 531