Adaptive Control Design and Analysis

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ISBN: 9780471274520 | 0471274526
Cover: Hardcover
Copyright: 7/9/2003

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A systematic and unified presentation of the fundamentals of adaptive control theory in both continuous time and discrete timeToday, adaptive control theory has grown to be a rigorous and mature discipline. As the advantages of adaptive systems for developing advanced applications grow apparent, adaptive control is becoming more popular in many fields of engineering and science. Using a simple, balanced, and harmonious style, this book provides a convenient introduction to the subject and improves one's understanding of adaptive control theory.Adaptive Control Design and Analysis features: Introduction to systems and control Stability, operator norms, and signal convergence Adaptive parameter estimation State feedback adaptive control designs Parametrization of state observers for adaptive control Unified continuous and discrete-time adaptive control L1+a robustness theory for adaptive systems Direct and indirect adaptive control designs Benchmark comparison study of adaptive control designs Multivariate adaptive control Nonlinear adaptive control Adaptive compensation of actuator nonlinearities End-of-chapter discussion, problems, and advanced topics As either a textbook or reference, this self-contained tutorial of adaptive control design and analysis is ideal for practicing engineers, researchers, and graduate students alike.

Preface

xiii

1 Introduction

(34)

1.1 Feedback in Control Systems

(2)

1.2 System Modeling

(3)

1.2.1 Continuous-Time Systems

(2)

1.2.2 Discrete-Time Systems

(1)

1.3 Feedback Control

(5)

1.4 Adaptive Control System Prototypes

(6)

1.5 Simple Adaptive Control Systems

(16)

1.5.1 Direct Adaptive Control

(4)

1.5.2 Indirect Adaptive Control

(2)

1.5.3 Discrete-Time Designs

(4)

1.5.4 Backstepping Nonlinear Design

(2)

1.5.5 Adaptive Control versus Fixed Control

(2)

1.5.6 Summary

(2)

Problems

(2)

2 Systems Theory

(61)

2.1 Dynamic System Models

(3)

2.1.1 Nonlinear Systems

(2)

2.1.2 Linear Systems

(1)

2.2 System Characterizations

(7)

2.3 Signal Measures

(4)

2.3.1 Vector and Matrix Norms

(3)

2.3.2 Signal Norms

(1)

2.4 Lyapunov Stability

(12)

2.4.1 Stability Definitions

(3)

2.4.2 Positive Definite Functions

(1)

2.4.3 Direct Method Lyapunov

(4)

2.4.4 Linear Systems

(3)

2.4.5 Lyapunov Indirect Method

(1)

2.5 Input-Output Stability

(19)

2.5.1 Lemma

(2)

2.5.2 Small-Gain Lemma

(4)

2.5.3 Operator Stability

(9)

2.5.4 Positive Real Strictly

(3)

2.6 Signal Convergence Lemmas

(4)

2.7 Discrete-Time Systems

(8)

2.7.1 System Modeling

(2)

2.7.2 Norms and Signal Spaces

(2)

2.7.3 Stability

(4)

2.8 Operator Norms

(2)

2.9 Pole Placement

(1)

Problems

(2)

3 Adaptive Parameter Estimation

(53)

3.1 A Parametrized System Model

(2)

3.2 Linear Parametric Models

101

(1)

3.3 Normalized Gradient Algorithm

102

(2)

3.4 Normalized Least-Squares Algorithm

104

(4)

3.5 Parameter Convergence

108

(6)

3.5.1 Persistency of Excitation

108

(2)

3.5.2 Convergence of the Gradient Algorithm

110

(1)

3.5.3 Convergence of the Least-Squares Algorithm

111

(3)

3.6 Discrete-Time Algorithms

114

(9)

3.6.1 Linear Parametric Models

114

(1)

3.6.2 Normalized Gradient Algorithm

115

(1)

3.6.3 Normalized Least-Squares Algorithm

116

(4)

3.6.4 Parameter Convergence

120

(3)

3.7 Robustness of Adaptive Algorithms

123

(5)

3.7.1 Continuous-Time Algorithms

123

(3)

3.7.2 Discrete-Time Algorithms

126

(2)

3.8 Robust Adaptive Lans

128

(12)

3.8.1 Continuous-Time Algorithms

128

(6)

3.8.2 Discrete-Time Algorithms

134

(5)

3.8.3 Summary

139

(1)

3.9 Discussion

140

(5)

Problems

145

(4)

4 Adaptive State Feedback Control

149

(46)

4.1 Design for State Tracking

149

(5)

4.1.1 Design Example

149

(2)

4.1.2 Control System Structure

151

(1)

4.1.3 Adaptive Laws

152

(2)

4.1.4 Adaptive System Properties

154

(1)

4.2 Design for Output Tracking

154

(5)

4.2.1 Introductory Example

154

(1)

4.2.2 Control System Structure

155

(3)

4.2.3 Adaptive Laws

158

(1)

4.3 Disturbance Rejection

159

(11)

4.3.1 State Tracking

159

(2)

4.3.2 Output Tracking

161

(9)

4.4 Parametrization of State Feedback

170

(4)

4.4.1 Parametrization with Full-Order Observer

170

(2)

4.4.2 Parametrization with Reduced-Order Observer

172

(2)

4.5 Discrete-Time Adaptive Control

174

(18)

4.5.1 Design Example

174

(3)

4.5.2 Output Tracking Design

177

(4)

4.5.3 Disturbance Rejection

181

(7)

4.5.4 Parametrizations of State Feedback

188

(4)

Problems

192

(3)

5 Continuous-Time Model Reference Adaptive Control

195

(76)

5.1 Control System Structure

195

(2)

5.2 Model Reference Control

197

(3)

5.3 Adaptive Control

200

(19)

5.3.1 Tracking Error Equation

201

(1)

5.3.2 Lyapunov Design for Relative Degree 1

201

(2)

5.3.3 Alternative Design for Relative Degree 1

203

(1)

5.3.4 Lyapunov Design for Arbitrary Relative Degrees

204

(7)

5.3.5 Gradient Design for Arbitrary Relative Degrees

211

(7)

5.3.6 Summary

218

(1)

5.4 Robustness of MRAC

219

(7)

5.4.1 Lyapunov Designs for Relative Degree 1

219

(2)

5.4.2 Gradient Algorithms

221

(5)

5.5 Robust MRAC

226

(13)

5.5.1 Modeling Errors

226

(2)

5.5.2 Robustness of MRC

228

(1)

5.5.3 Robust Adaptive Laws

229

(2)

5.5.4 Robust Stability Analysis

231

(7)

5.5.5 Summary

238

(1)

5.6 Design for Unknown High Frequency Gain

239

(15)

5.6.1 Adaptive Control Designs Using Nussbaum Gain

239

(7)

5.6.2 An Adaptive Control System

246

(8)

5.7 Discussion

254

(10)

Problems

264

(7)

6 Discrete-Time Model Reference Adaptive Control

271

(24)

6.1 Control System Structure

271

(2)

6.2 Model Reference Control

273

(4)

6.3 Adaptive Control Systems

277

(9)

6.3.1 Adaptive Control for Disturbance d(t)=0

278

(2)

6.3.2 Robustness of MRAC with d(t) € L2

280

(1)

6.3.3 Robust Adaptation for Bounded d(t)

281

(5)

6.4 Robustness of MRAC with L1+a Errors

286

(8)

6.4.1 Plant with Modeling Errors

286

(1)

6.4.2 Adaptive Control Scheme

287

(1)

6.4.3 Robustness Analysis

288

(5)

6.4.4 Discussion

293

(1)

Problems

294

(1)

7 Indirect Adaptive Control

295

(54)

7.1 Model Reference Designs

295

(17)

7.1.1 Simple Adaptive Control Systems

296

(7)

7.1.2 General Design Procedure

303

(9)

7.2 Pole Placement Designs

312

(16)

7.2.1 Control System Structure

312

(4)

7.2.2 Pole Placement Control

316

(1)

7.2.3 Controller Parameter Adaptation

317

(11)

7.3 Discrete-Time Adaptive Control Systems

328

(15)

7.3.1 Model Reference Designs

328

(8)

7.3.2 Pole Placement Designs

336

(7)

7.4 Discussion

343

(4)

Problems

347

(2)

8 A Comparison Study

349

(22)

8.1 Benchmark Example

349

(2)

8.2 Direct Adaptive Control Designs

351

(1)

8.2.1 State Feedback Design

351

(1)

8.2.2 Output Feedback Design

352

(1)

8.3 Indirect Adaptive Control Design

352

(1)

8.4 Direct-Indirect Adaptive Control Design

353

(12)

8.4.1 Direct Adaptive Control for Motor Dynamics

353

(2)

8.4.2 Indirect Adaptive Control for Load Dynamics

355

(10)

8.4.3 Simulation Results

365

(1)

8.5 Adaptive Backstepping Design

365

(5)

Problems

370

(1)

9 Multivariable Adaptive Control

371

(134)

9.1 Adaptive State Feedback Control

371

(10)

9.1.1 Design for State Tracking

372

(3)

9.1.2 Design Based on LDU Parametrization

375

(3)

9.1.3 System Identification

378

(3)

9.2 Model Reference Adaptive Control

381

(76)

9.2.1 Description of Multivariable Systems

381

(3)

9.2.2 Plant and Controller Parametrizations

384

(10)

9.2.3 Robust Model Reference Control

394

(1)

9.2.4 Error Model

395

(2)

9.2.5 Adaptive Laws

397

(5)

9.2.6 Stability and Robustness Analysis

402

(11)

9.2.7 MRAC Using Right Interactor Matrices

413

(3)

9.2.8 Continuous-Time Lyapunov Designs

416

(13)

9.2.9 MRAC Designs for Input and Output Delays

429

(10)

9.2.10 Adaptation and High Frequency Gain Matrix

439

(2)

9.2.11 Designs Based on Decompositions of Kp

441

(16)

9.3 Adaptive Backstepping Control

457

(20)

9.3.1 Plant Parametrization

458

(1)

9.3.2 State Observer

459

(3)

9.3.3 Design Procedure for Bm Nonsingular

462

(7)

9.3.4 Design Based on SDU Decomposition of Bm

469

(3)

9.3.5 Design Procedure for Bm Singular

472

(5)

9.4 Adaptive Control of Robotic Systems

477

(12)

9.4.1 Robotic System Modeling

477

(3)

9.4.2 Illustrative Example

480

(2)

9.4.3 Design for Parameter Variations

482

(3)

9.4.4 Design for Unmodeled Dynamics

485

(4)

9.5 Discussion

489

(8)

Problems

497

(8)

10 Adaptive Control of Systems with Nonlinearities

505

(72)

10.1 Actuator Nonlinearity Compensation

506

(7)

10.1.1 Actuator Nonlinearities

506

(3)

10.1.2 Parametrized Nonlinearity Inverses

509

(4)

10.2 State Feedback Inverse Control

513

(5)

10.3 Output Feedback Inverse Control

518

(6)

10.4 Designs for Multivariable Systems

524

(6)

10.5 Designs for Unknown Linear Dynamics

530

(5)

10.5.1 Designs for SISO Plants

530

(2)

10.5.2 Designs for MIMO Plants

532

(3)

10.6 Designs for Nonlinear Dynamics

535

(37)

10.6.1 Design for Feedback Linearizable Systems

536

(9)

10.6.2 Design for Parametric-Strict-Feedback Systems

545

(7)

10.6.3 Design for Output-Feedback Systems

552

(20)

10.7 Discussion

572

(1)

Problems

573

(4)

Bibliography

577

(38)

Index

615

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Adaptive Control Design and Analysis

Summary

Author Biography

Table of Contents

Supplemental Materials