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El. knyga: System Identification with Quantized Observations

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This book presents recently developed methodologies that utilize quantized information in system identification and explores their potential in extending control capabilities for systems with limited sensor information or networked systems. The results of these methodologies can be applied to signal processing and control design of communication and computer networks, sensor networks, mobile agents, coordinated data fusion, remote sensing, telemedicine, and other fields in which noise-corrupted quantized data need to be processed.

Providing a comprehensive coverage of quantized identification, the book treats linear and nonlinear systems, as well as time-invariant and time-varying systems. The authors examine independent and dependent noises, stochastic- and deterministic-bounded noises, and also noises with unknown distribution functions. The key methodologies combine empirical measures and information-theoretic approaches to derive identification algorithms, provide convergence and convergence speed, establish efficiency of estimation, and explore input design, threshold selection and adaptation, and complexity analysis.

System Identification with Quantized Observations is an excellent resource for graduate students, systems theorists, control engineers, applied mathematicians, as well as practitioners who use identification algorithms in their work. Selected material from the book may be used in graduate-level courses on system identification.

Recenzijos

From the reviews:

The central idea in this book is to provide a comprehensive treatment of both theory and algorithms needed for parameter identification of systems with quantized observations. the book conveys a clear and very complete overview of recent exciting developments in the area of identification with quantized observations. It is meant as a state-of-the-art book . All this makes the book an extremely valuable resource for researchers and engineers interested in modern system identification. (Dariusz Uciski, Mathematical Reviews, Issue 2011 i)

Preface xiii
Conventions xv
Glossary of Symbols xvii
Part I Overview
1(22)
1 Introduction
3(10)
1.1 Motivating Examples
4(3)
1.2 System Identification with Quantized Observations
7(1)
1.3 Outline of the Book
8(5)
2 System Settings
13(10)
2.1 Basic Systems
14(2)
2.2 Quantized Output Observations
16(1)
2.3 Inputs
17(1)
2.4 System Configurations
18(2)
2.4.1 Filtering and Feedback Configurations
19(1)
2.4.2 Systems with Communication Channels
19(1)
2.5 Uncertainties
20(2)
2.5.1 System Uncertainties: Unmodeled Dynamics
20(1)
2.5.2 System Uncertainties: Function Mismatch
21(1)
2.5.3 Sensor Bias and Drifts
21(1)
2.5.4 Noise
21(1)
2.5.5 Unknown Noise Characteristics
22(1)
2.5.6 Communication Channel Uncertainties
22(1)
2.6 Notes
22(1)
Part II Stochastic Methods for Linear Systems
23(94)
3 Empirical-Measure-Based Identification
25(24)
3.1 An Overview of Empirical-Measure-Based Identification
26(3)
3.2 Empirical Measures and Identification Algorithms
29(3)
3.3 Strong Convergence
32(2)
3.4 Asymptotic Distributions
34(3)
3.5 Mean-Square Convergence
37(4)
3.6 Convergence under Dependent Noise
41(2)
3.7 Proofs of Two Propositions
43(3)
3.8 Notes
46(3)
4 Estimation Error Bounds: Including Unmodeled Dynamics
49(10)
4.1 Worst-Case Probabilistic Errors and Time Complexity
50(1)
4.2 Upper Bounds on Estimation Errors and Time Complexity
50(3)
4.3 Lower Bounds on Estimation Errors
53(3)
4.4 Notes
56(3)
5 Rational Systems
59(8)
5.1 Preliminaries
59(1)
5.2 Estimation of Ik
60(2)
5.3 Estimation of Parameter θ
62(4)
5.3.1 Parameter Identifiability
62(3)
5.3.2 Identification Algorithms and Convergence Analysis
65(1)
5.4 Notes
66(1)
6 Quantized Identification and Asymptotic Efficiency
67(14)
6.1 Basic Algorithms and Convergence
68(2)
6.2 Quasi-Convex Combination Estimators (QCCE)
70(2)
6.3 Alternative Covariance Expressions of Optimal QCCEs
72(3)
6.4 Cramer-Rao Lower Bounds and Asymptotic Efficiency of the Optimal QCCE
75(4)
6.5 Notes
79(2)
7 Input Design for Identification in Connected Systems
81(14)
7.1 Invariance of Input Periodicity and Rank in Open- and Closed-Loop Configurations
82(1)
7.2 Periodic Dithers
83(2)
7.3 Sufficient Richness Conditions under Input Noise
85(3)
7.4 Actuator Noise
88(3)
7.5 Notes
91(4)
8 Identification of Sensor Thresholds and Noise Distribution Functions
95(22)
8.1 Identification of Unknown Thresholds
95(4)
8.1.1 Sufficient Richness Conditions
96(3)
8.1.2 Recursive Algorithms
99(1)
8.2 Parameterized Distribution Functions
99(2)
8.3 Joint Identification Problems
101(1)
8.4 Richness Conditions for Joint Identification
101(2)
8.5 Algorithms for Identifying System Parameters and Distribution Functions
103(2)
8.6 Convergence Analysis
105(1)
8.7 Recursive Algorithms
106(5)
8.7.1 Recursive Schemes
107(1)
8.7.2 Asymptotic Properties of Recursive Algorithm (8.14)
108(3)
8.8 Algorithm Flowcharts
111(2)
8.9 Illustrative Examples
113(2)
8.10 Notes
115(2)
Part III Deterministic Methods for Linear Systems
117(54)
9 Worst-Case Identification
119(30)
9.1 Worst-Case Uncertainty Measures
120(1)
9.2 Lower Bounds on Identification Errors and Time Complexity
121(3)
9.3 Upper Bounds on Time Complexity
124(3)
9.4 Identification of Gains
127(8)
9.5 Identification Using Combined Deterministic and Stochastic Methods
135(10)
9.5.1 Identifiability Conditions and Properties under Deterministic and Stochastic Frameworks
136(3)
9.5.2 Combined Deterministic and Stochastic Identification Methods
139(2)
9.5.3 Optimal Input Design and Convergence Speed under Typical Distributions
141(4)
9.6 Notes
145(4)
10 Worst-Case Identification Using Quantized Observations
149(22)
10.1 Worst-Case Identification with Quantized Observations
150(1)
10.2 Input Design for Parameter Decoupling
151(2)
10.3 Identification of Single-Parameter Systems
153(10)
10.3.1 General Quantization
154(5)
10.3.2 Uniform Quantization
159(4)
10.4 Time Complexity
163(2)
10.5 Examples
165(3)
10.6 Notes
168(3)
Part IV Identification of Nonlinear and Switching Systems
171(82)
11 Identification of Wiener Systems
173(24)
11.1 Wiener Systems
174(1)
11.2 Basic Input Design and Core Identification Problems
175(2)
11.3 Properties of Inputs and Systems
177(2)
11.4 Identification Algorithms
179(5)
11.5 Asymptotic Efficiency of the Core Identification Algorithms
184(4)
11.6 Recursive Algorithms and Convergence
188(2)
11.7 Examples
190(4)
11.8 Notes
194(3)
12 Identification of Hammerstein Systems
197(28)
12.1 Problem Formulation
198(1)
12.2 Input Design and Strong-Full-Rank Signals
199(3)
12.3 Estimates of ζ with Individual Thresholds
202(2)
12.4 Quasi-Convex Combination Estimators of ζ
204(8)
12.5 Estimation of System Parameters
212(6)
12.6 Examples
218(4)
12.7 Notes
222(3)
13 Systems with Markovian Parameters
225(28)
13.1 Markov Switching Systems with Binary Observations
227(1)
13.2 Wonham-Type Filters
227(2)
13.3 Tracking: Mean-Square Criteria
229(8)
13.4 Tracking Infrequently Switching Systems: MAP Methods
237(5)
13.5 Tracking Fast-Switching Systems
242(10)
13.5.1 Long-Run Average Behavior
243(2)
13.5.2 Empirical Measure-Based Estimators
245(4)
13.5.3 Estimation Errors on Empirical Measures: Upper and Lower Bounds
249(3)
13.6 Notes
252(1)
Part V Complexity Analysis
253(34)
14 Complexities, Threshold Selection, Adaptation
255(20)
14.1 Space and Time Complexities
256(3)
14.2 Binary Sensor Threshold Selection and Input Design
259(2)
14.3 Worst-Case Optimal Threshold Design
261(3)
14.4 Threshold Adaptation
264(3)
14.5 Quantized Sensors and Optimal Resource Allocation
267(4)
14.6 Discussions on Space and Time Complexity
271(1)
14.7 Notes
272(3)
15 Impact of Communication Channels
275(12)
15.1 Identification with Communication Channels
276(1)
15.2 Monotonicity of Fisher Information
277(1)
15.3 Fisher Information Ratio of Communication Channels
278(2)
15.4 Vector-Valued Parameters
280(2)
15.5 Relationship to Shannon's Mutual Information
282(1)
15.6 Tradeoff between Time Information and Space Information
283(1)
15.7 Interconnections of Communication Channels
284(1)
15.8 Notes
285(2)
A Background Materials
287(18)
A.1 Martingales
287(3)
A.2 Markov Chains
290(9)
A.3 Weak Convergence
299(3)
A.4 Miscellany
302(3)
References 305(10)
Index 315
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