Optimal Control

by Lewis, Frank L.; Vrabie, Draguna; Syrmos, Vassilis L.

• ISBN13: 9780470633496
• ISBN10: 0470633492
• Edition: 3rd
• Format: Hardcover
• Copyright: 2012-02-01
• Publisher: Wiley

Summary

This new, updated edition of Optimal Control reflects major changes that have occurred in the field in recent years and presents, in a clear and direct way, the fundamentals of optimal control theory. It covers the major topics involving measurement, principles of optimality, dynamic programming, variational methods, Kalman filtering, and other solution techniques. To give the reader a sense of the problems that can arise in a hands-on project, the authors have updated material on optimal output feedback control, a technique used in the aerospace industry. Also included is a new chapter on Reinforcement Learning for adaptive optimal control. Relations to classical control theory are emphasized throughout the text, and a root-locus approach to steady-state controller design is included. A chapter on optimal control of polynomial systems is designed to give the reader sufficient background for further study in the field of adaptive control.

Author Biography

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.

Table of Contents

Preface	p. xi
Static Optimization	p. 1
Optimization without Constraints	p. 1
Optimization with Equality Constraints	p. 4
Numerical Solution Methods	p. 15
Problems	p. 15
Optimal Control of Discrete-Time Systems	p. 19
Solution of the General Discrete-Time Optimization Problem	p. 19
Discrete-Time Linear Quadratic Regulator	p. 32
Digital Control of Continuous-Time Systems	p. 53
Steady-State Closed-Loop Control and Suboptimal Feedback	p. 65
Frequency-Domain Results	p. 96
Problems	p. 102
Optimal Control of Continuous-Time Systems	p. 110
The Calculus of Variations	p. 110
Solution of the General Continuous-Time Optimization Problem	p. 112
Continuous-Time Linear Quadratic Regulator	p. 135
Steady-State Closed-Loop Control and Suboptimal Feedback	p. 154
Frequency-Domain Results	p. 164
Problems	p. 167
The Tracking Problem and Other LQR Extensions	p. 177
The Tracking Problem	p. 177
Regulator with Function of Final State Fixed	p. 183
Second-Order Variations in the Performance Index	p. 185
The Discrete-Time Tracking Problem	p. 190
Discrete Regulator with Function of Final State Fixed	p. 199
Discrete Second-Order Variations in the Performance Index	p. 206
Problems	p. 211
Final-Time-Free and Constrained Input Control	p. 213
Final-Time-Free Problems	p. 213
Constrained Input Problems	p. 232
Problems	p. 257
Dynamic Programming	p. 260
Bellman's Principle of Optimality	p. 260
Discrete-Time Systems	p. 263
Continuous-Time Systems	p. 271
Problems	p. 283
Optimal Control for Polynomial Systems	p. 287
Discrete Linear Quadratic Regulator	p. 287
Digital Control of Continuous-Time Systems	p. 292
Problems	p. 295
Output Feedback and Structured Control	p. 297
Linear Quadratic Regulator with Output Feedback	p. 297
Tracking a Reference Input	p. 313
Tracking by Regulator Redesign	p. 327
Command-Generator Tracker	p. 331
Explicit Model-Following Design	p. 338
Output Feedback in Game Theory and Decentralized Control	p. 343
Problems	p. 351
Robustness and Multivariable Frequency-Domain Techniques	p. 355
Introduction	p. 355
Multivariable Frequency-Domain Analysis	p. 357
Robust Output-Feedback Design	p. 380
Observers and the Kalman Filter	p. 383
LQG/Loop-Transfer Recovery	p. 408
H∞ DESIGN	p. 430
Problems	p. 435
Differential Games	p. 438
Optimal Control Derived Using Pontryagin's Minimum Principle and the Bellman Equation	p. 439
Two-player Zero-sum Games	p. 444
Application of Zero-sum Games to H∞ Control	p. 450
Multiplayer Non-zero-sum Games	p. 453
Reinforcement Learning and Optimal Adaptive Control	p. 461
Reinforcement Learning	p. 462
Markov Decision Processes	p. 464
Policy Evaluation and Policy Improvement	p. 474
Temporal Difference Learning and Optimal Adaptive Control	p. 489
Optimal Adaptive Control for Discrete-time Systems	p. 490
Integral Reinforcement Learning for Optimal Adaptive Control of Continuous-time Systems	p. 503
Synchronous Optimal Adaptive Control for Continuous-time Systems	p. 513
Review of Matrix Algebra	p. 518
Basic Definitions and Facts	p. 518
Partitioned Matrices	p. 519
Quadratic Forms and Definiteness	p. 521
Matrix Calculus	p. 523
The Generalized Eigenvalue Problem	p. 525
References	p. 527
Index	p. 535
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