Adaptive Control

Stability, Convergence and Robustness

By: SHANKAR SASTRY

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Paperback | 14 September 2011

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With a focus on linear, continuous time, single-input, single-output systems, this volume surveys the major results and techniques of analysis in the field of adaptive control. The authors offer a clear, conceptual presentation of adaptive methods, enabling a critical evaluation of these techniques and suggesting avenues of further development.

A brief historical overview of adaptive control is followed by a review of mathematical preliminaries and the development of several adaptive identification algorithms. Succeeding chapters examine averaging techniques, the robustness of adaptive schemes, and advanced topics — including the use of prior information and multivariable adaptive control — followed by a concise introduction to the control of a class of nonlinear systems. The treatment is largely self-contained, assuming only some graduate-level background in basic control systems and in linear systems theory.

Reprint of the Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1989 edition.

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Non-Fiction Engineering & Technology Technology in General Engineering in General Religion & Beliefs Electronics & Communications Engineering Electronics Engineering Automatic Control Engineering Robotics Energy Technology & Engineering Electrical Engineering

Preface	p. xiii
Introduction	p. 1
Identification and Adaptive Control	p. 1
Approaches to Adaptive Control	p. 4
Gain Scheduling	p. 4
Model Reference Adaptive Systems	p. 5
Self Tuning Regulators	p. 8
Stochastic Adaptive Control	p. 9
A Simple Example	p. 11
Preliminaries	p. 17
Notation	p. 17
L_p Spaces, Norms	p. 18
Positive Definite Matrices	p. 19
Stability of Dynamic Systems	p. 20
Differential Equations	p. 20
Stability Definitions	p. 23
Lyapunov Stability Theory	p. 25
Exponential Stability Theorems	p. 28
Exponential Stability of Nonlinear Systems	p. 28
Exponential Stability of Linear Time-Varying Systems	p. 32
Exponential Stability of Linear Time Invariant Systems	p. 38
Generalized Harmonic Analysis	p. 39
Identification	p. 45
Introduction	p. 45
Identification Problem	p. 52
Identifier Structure	p. 53
Linear Error Equation and Identification Algorithms	p. 57
Gradient Algorithms	p. 58
Least-Squares Algorithms	p. 61
Properties of the Identification Algorithms-Identifier Stability	p. 63
Gradient Algorithms	p. 63
Least-Squares Algorithms	p. 66
Stability of the Identifier	p. 69
Persistent Excitation and Exponential Parameter Convergence	p. 71
Model Reference Identifiers-SPR Error Equation	p. 76
Model Reference Identifiers	p. 76
Strictly Positive Real Error Equation and Identification Algorithms	p. 82
Exponential Convergence of the Gradient Algorithms with SPR Error Equations	p. 85
Frequency Domain Conditions for Parameter Convergence	p. 90
Parameter Convergence	p. 90
Partial Parameter Convergence	p. 95
Conclusions	p. 98
Adaptive Control	p. 99
Introduction	p. 99
Model Reference Adaptive Control Problem	p. 103
Controller Structure	p. 104
Adaptive Control Schemes	p. 110
Input Error Direct Adaptive Control	p. 111
Output Error Direct Adaptive Control	p. 118
Indirect Adaptive Control	p. 123
Alternate Model Reference Schemes	p. 127
Adaptive Pole Placement Control	p. 129
The Stability! Problem in Adaptive Control	p. 130
Analysis of the Model Reference Adaptive Control System	p. 132
Useful Lemmas	p. 138
Stability Proofs	p. 142
Stability-Input Error Direct Adaptive Control	p. 142
Stability-Output Error Direct Adaptive Control	p. 149
Stability-Indirect Adaptive Control	p. 151
Exponential Parameter Convergence	p. 154
Conclusions	p. 156
Parameter Convergence Using Averaging Techniques	p. 158
Introduction	p. 158
Examples of Averaging Analysis	p. 159
Averaging Theory-One-Time Scale	p. 166
Application to Identification	p. 175
Averaging Theory-Two-Time Scales	p. 179
Separated Time Scales	p. 183
Mixed Time Scales	p. 186
Applications to Adaptive Control	p. 187
Output Error Scheme-Linearized Equations	p. 188
Output Error Scheme-Nonlinear Equations	p. 192
Input Error Scheme	p. 202
Conclusions	p. 207
Robustness	p. 209
Structured and Unstructured Uncertainty	p. 209
The Rohrs Examples	p. 215
Robustness of Adaptive Algorithms with Persistency of Excitation	p. 219
Exponential Convergence and Robustness	p. 221
Robustness of an Adaptive Control Scheme	p. 225
Heuristic Analysis of the Rohrs Examples	p. 231
Averaging Analysis of Slow Drift Instability	p. 236
Instability Theorems Using Averaging	p. 236
Application to the Output Error Scheme	p. 241
Methods for Improving Robustness-Qualitative Discussion	p. 248
Robust Identification Schemes	p. 248
Specification of the Closed Loop Control Objective-Choice of Control Model and of Reference Input	p. 250
The Usage of Prior Information	p. 250
Time Variation of Parameters	p. 251
Robustness via Update Law Modifications	p. 251
Deadzone and Relative Deadzone	p. 251
Leakage Term (-Modification)	p. 253
Regressor Vector Filtering	p. 253
Slow Adaptation, Averaging and Hybrid Update Laws	p. 254
Conclusions	p. 254
Advanced Topics in Identification and Adaptive Control	p. 257
Use of Prior Information	p. 257
Identification of Partially Known Systems	p. 257
Effect of Unmodeled Dynamics	p. 263
Global Stability of Indirect Adaptive Control Schemes	p. 266
Indirect Adaptive Control Scheme	p. 267
Indirect Adaptive Pole Placement	p. 272
Indirect Adaptive Stabilization-The Factorization Approach	p. 274
Multivariate Adaptive Control	p. 277
Introduction	p. 277
Preliminaries	p. 278
Factorization of Transfer Function Matrices	p. 278
Interactor Matrix and Hermite Form	p. 282
Model Reference Adaptive Control-Controller Structure	p. 286
Model Reference Adaptive Control-Input Error Scheme	p. 290
Alternate Schemes	p. 292
Conclusions	p. 293
Adaptive Control of a Class of Nonlinear Systems	p. 294
Introduction	p. 294
Linearizing Control for a Class of Nonlinear Systems-A Review	p. 295
Basic Theory	p. 295
Minimum Phase Nonlinear Systems	p. 299
The Single-Input Single-Output Case	p. 300
The Multi-Input Multi-Output Case	p. 305
Model Reference Control for Nonlinear Systems	p. 307
Adaptive Control of Linearizable Minimum Phase Systems	p. 309
Single-Input Single-Output, Relative Degree One Case	p. 309
Extensions to Higher Relative Degree SISO Systems	p. 312
Adaptive Control of MIMO Systems Decouplable by Static State Feedback	p. 320
Conclusions	p. 322
Conclusions	p. 324
General Conclusions	p. 325
Future Research	p. 325
Appendix	p. 331
References	p. 359
Index	p. 373
Errata	p. 379
Table of Contents provided by Ingram. All Rights Reserved.

Adaptive Control

Stability, Convergence and Robustness

At a Glance

Paperback

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