System Identification With Quantized

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.

Preface	p. xiii
Conventions	p. xv
Glossary of Symbols	p. xvii
Overview	p. 1
Introduction	p. 3
Motivating Examples	p. 4
System Identification with Quantized Observations	p. 7
Outline of the Book	p. 8
System Settings	p. 13
Basic Systems	p. 14
Quantized Output Observations	p. 16
Inputs	p. 17
System Configurations	p. 18
Filtering and Feedback Configurations	p. 19
Systems with Communication Channels	p. 19
Uncertainties	p. 20
System Uncertainties: Unmodeled Dynamics	p. 20
System Uncertainties: Function Mismatch	p. 21
Sensor Bias and Drifts	p. 21
Noise	p. 21
Unknown Noise Characteristics	p. 22
Communication Channel Uncertainties	p. 22
Notes	p. 22
Stochastic Methods for Linear Systems	p. 23
Empirical-Measure-Based Identification	p. 25
An Overview of Empirical-Measure-Based Identification	p. 26
Empirical Measures and Identification Algorithms	p. 29
Strong Convergence	p. 32
Asymptotic Distributions	p. 34
Mean-Square Convergence	p. 37
Convergence under Dependent Noise	p. 41
Proofs of Two Propositions	p. 43
Notes	p. 46
Estimation Error Bounds: Including Unmodeled Dynamics	p. 49
Worst-Case Probabilistic Errors and Time Complexity	p. 50
Upper Bounds on Estimation Errors and Time Complexity	p. 50
Lower Bounds on Estimation Errors	p. 53
Notes	p. 56
Rational Systems	p. 59
Preliminaries	p. 59
Estimation of x_k	p. 60
Estimation of Parameter ¿	p. 62
Parameter Identifiability	p. 62
Identification Algorithms and Convergence Analysis	p. 65
Notes	p. 66
Quantized Identification and Asymptotic Efficiency	p. 67
Basic Algorithms and Convergence	p. 68
Quasi-Convex Combination Estimators (QCCE)	p. 70
Alternative Covariance Expressions of Optimal QCCEs	p. 72
Cramér-Rao Lower Bounds and Asymptotic Efficiency of the Optimal QCCE	p. 75
Notes	p. 79
Input Design for Identification in Connected Systems	p. 81
Invariance of Input Periodicity and Rank in Open- and Closed-Loop Configurations	p. 82
Periodic Dithers	p. 83
Sufficient Richness Conditions under Input Noise	p. 85
Actuator Noise	p. 88
Notes	p. 91
Identification of Sensor Thresholds and Noise Distribution Functions	p. 95
Identification of Unknown Thresholds	p. 95
Sufficient Richness Conditions	p. 96
Recursive Algorithms	p. 99
Parameterized Distribution Functions	p. 99
Joint Identification Problems	p. 101
Richness Conditions for Joint Identification	p. 101
Algorithms for Identifying System Parameters and Distribution Functions	p. 103
Convergence Analysis	p. 105
Recursive Algorithms	p. 106
Recursive Schemes	p. 107
Asymptotic Properties of Recursive Algorithm (8.14)	p. 108
Algorithm Flowcharts	p. 111
Illustrative Examples	p. 113
Notes	p. 115
Deterministic Methods for Linear Systems	p. 117
Worst-Case Identification	p. 119
Worst-Case Uncertainty Measures	p. 120
Lower Bounds on Identification Errors and Time Complexity	p. 121
Upper Bounds on Time Complexity	p. 124
Identification of Gains	p. 127
Identification Using Combined Deterministic and Stochastic Methods	p. 135
Identifiability Conditions and Properties under Deterministic and Stochastic Frameworks	p. 136
Combined Deterministic and Stochastic Identification Methods	p. 139
Optimal Input Design and Convergence Speed under Typical Distributions	p. 141
Notes	p. 145
Worst-Case Identification Using Quantized Observations	p. 149
Worst-Case Identification with Quantized Observations	p. 150
Input Design for Parameter Decoupling	p. 151
Identification of Single-Parameter Systems	p. 153
General Quantization	p. 154
Uniform Quantization	p. 159
Time Complexity	p. 163
Examples	p. 165
Notes	p. 168
Identification of Nonlinear and Switching Systems	p. 171
Identification of Wiener Systems	p. 173
Wiener Systems	p. 174
Basic Input Design and Core Identification Problems	p. 175
Properties of Inputs and Systems	p. 177
Identification Algorithms	p. 179
Asymptotic Efficiency of the Core Identification Algorithms	p. 184
Recursive Algorithms and Convergence	p. 188
Examples	p. 190
Notes	p. 194
Identification of Hammerstein Systems	p. 197
Problem Formulation	p. 198
Input Design and Strong-Full-Rank Signals	p. 199
Estimates of ¿ with Individual Thresholds	p. 202
Quasi-Convex Combination Estimators of ¿	p. 204
Estimation of System Parameters	p. 212
Examples	p. 218
Notes	p. 222
Systems with Markovian Parameters	p. 225
Markov Switching Systems with Binary Observations	p. 227
Wonham-Type Filters	p. 227
Tracking: Mean-Square Criteria	p. 229
Tracking Infrequently Switching Systems: MAP Methods	p. 237
Tracking Fast-Switching Systems	p. 242
Long-Run Average Behavior	p. 243
Empirical Measure-Based Estimators	p. 245
Estimation Errors on Empirical Measures: Upper and Lower Bounds	p. 249
Notes	p. 252
Complexity Analysis	p. 253
Complexities, Threshold Selection, Adaptation	p. 255
Space and Time Complexities	p. 256
Binary Sensor Threshold Selection and Input Design	p. 259
Worst-Case Optimal Threshold Design	p. 261
Threshold Adaptation	p. 264
Quantized Sensors and Optimal Resource Allocation	p. 267
Discussions on Space and Time Complexity	p. 271
Notes	p. 272
Impact of Communication Channels	p. 275
Identification with Communication Channels	p. 276
Monotonicity of Fisher Information	p. 277
Fisher Information Ratio of Communication Channels	p. 278
Vector-Valued Parameters	p. 280
Relationship to Shannon's Mutual Information	p. 282
Tradeoff between Time Information and Space Information	p. 283
Interconnections of Communication Channels	p. 284
Notes	p. 285
Background Materials	p. 287
Martingales	p. 287
Markov Chains	p. 290
Weak Convergence	p. 299
Miscellany	p. 302
References	p. 305
Index	p. 315
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System Identification With Quantized Observations

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