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Optimal Control, 3rd Edition

ISBN: 978-0-470-63349-6
552 pages
February 2012
Optimal Control, 3rd Edition (0470633492) cover image

A new edition of the classic text on optimal control theory

As a superb introductory text and an indispensable reference, this new edition of Optimal Control will serve the needs of both the professional engineer and the advanced student in mechanical, electrical, and aerospace engineering. Its coverage encompasses all the fundamental topics as well as the major changes that have occurred in recent years. An abundance of computer simulations using MATLAB and relevant Toolboxes is included to give the reader the actual experience of applying the theory to real-world situations. Major topics covered include:

  • Static Optimization

  • Optimal Control of Discrete-Time Systems

  • Optimal Control of Continuous-Time Systems

  • The Tracking Problem and Other LQR Extensions

  • Final-Time-Free and Constrained Input Control

  • Dynamic Programming

  • Optimal Control for Polynomial Systems

  • Output Feedback and Structured Control

  • Robustness and Multivariable Frequency-Domain Techniques

  • Differential Games

  • Reinforcement Learning and Optimal Adaptive Control

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PREFACE xi

1 STATIC OPTIMIZATION 1

1.1 Optimization without Constraints / 1

1.2 Optimization with Equality Constraints / 4

1.3 Numerical Solution Methods / 15

Problems / 15

2 OPTIMAL CONTROL OF DISCRETE-TIME SYSTEMS 19

2.1 Solution of the General Discrete-Time Optimization Problem / 19

2.2 Discrete-Time Linear Quadratic Regulator / 32

2.3 Digital Control of Continuous-Time Systems / 53

2.4 Steady-State Closed-Loop Control and Suboptimal Feedback / 65

2.5 Frequency-Domain Results / 96

Problems / 102

3 OPTIMAL CONTROL OF CONTINUOUS-TIME SYSTEMS 110

3.1 The Calculus of Variations / 110

3.2 Solution of the General Continuous-Time Optimization Problem / 112

3.3 Continuous-Time Linear Quadratic Regulator / 135

3.4 Steady-State Closed-Loop Control and Suboptimal Feedback / 154

3.5 Frequency-Domain Results / 164

Problems / 167

4 THE TRACKING PROBLEM AND OTHER LQR EXTENSIONS 177

4.1 The Tracking Problem / 177

4.2 Regulator with Function of Final State Fixed / 183

4.3 Second-Order Variations in the Performance Index / 185

4.4 The Discrete-Time Tracking Problem / 190

4.5 Discrete Regulator with Function of Final State Fixed / 199

4.6 Discrete Second-Order Variations in the Performance Index / 206

Problems / 211

5 FINAL-TIME-FREE AND CONSTRAINED INPUT CONTROL 213

5.1 Final-Time-Free Problems / 213

5.2 Constrained Input Problems / 232

Problems / 257

6 DYNAMIC PROGRAMMING 260

6.1 Bellman’s Principle of Optimality / 260

6.2 Discrete-Time Systems / 263

6.3 Continuous-Time Systems / 271

Problems / 283

7 OPTIMAL CONTROL FOR POLYNOMIAL SYSTEMS 287

7.1 Discrete Linear Quadratic Regulator / 287

7.2 Digital Control of Continuous-Time Systems / 292

Problems / 295

8 OUTPUT FEEDBACK AND STRUCTURED CONTROL 297

8.1 Linear Quadratic Regulator with Output Feedback / 297

8.2 Tracking a Reference Input / 313

8.3 Tracking by Regulator Redesign / 327

8.4 Command-Generator Tracker / 331

8.5 Explicit Model-Following Design / 338

8.6 Output Feedback in Game Theory and Decentralized Control / 343

Problems / 351

9 ROBUSTNESS AND MULTIVARIABLE FREQUENCY-DOMAIN TECHNIQUES 355

9.1 Introduction / 355

9.2 Multivariable Frequency-Domain Analysis / 357

9.3 Robust Output-Feedback Design / 380

9.4 Observers and the Kalman Filter / 383

9.5 LQG/Loop-Transfer Recovery / 408

9.6 H∞ DESIGN / 430

Problems / 435

10 DIFFERENTIAL GAMES 438

10.1 Optimal Control Derived Using Pontryagin’s Minimum Principle and the Bellman Equation / 439

10.2 Two-player Zero-sum Games / 444

10.3 Application of Zero-sum Games to H∞ Control / 450

10.4 Multiplayer Non-zero-sum Games / 453

11 REINFORCEMENT LEARNING AND OPTIMAL ADAPTIVE CONTROL 461

11.1 Reinforcement Learning / 462

11.2 Markov Decision Processes / 464

11.3 Policy Evaluation and Policy Improvement / 474

11.4 Temporal Difference Learning and Optimal Adaptive Control / 489

11.5 Optimal Adaptive Control for Discrete-time Systems / 490

11.6 Integral Reinforcement Learning for Optimal Adaptive Control of Continuous-time Systems / 503

11.7 Synchronous Optimal Adaptive Control for Continuous-time Systems / 513

APPENDIX A REVIEW OF MATRIX ALGEBRA 518

A.1 Basic Definitions and Facts / 518

A.2 Partitioned Matrices / 519

A.3 Quadratic Forms and Definiteness / 521

A.4 Matrix Calculus / 523

A.5 The Generalized Eigenvalue Problem / 525

REFERENCES 527

INDEX 535

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FRANK L. LEWIS is the Moncrief-O'Donnell Professor and Head of the Advanced Controls, Sensors, and MEMS Group in the Automation and Robotics Research Institute of the University of Texas at Arlington. Dr. Lewis is also a Fellow of the IEEE.

DRAGUNA L. VRABIE is Graduate Research Assistant in Electrical Engineering at the University of Texas at Arlington, specializing in approximate dynamic programming for continuous state and action spaces, optimal control, adaptive control, model predictive control, and general theory of nonlinear systems.

VASSILIS L. SYRMOS is a Professor in the Department of Electrical Engineering and the Associate Vice Chancellor for Research and Graduate Education at the University of Hawaii at Manoa.

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