Optimal Control
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Optimal Control

Optimal Control


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About the Book

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

Table of Contents:
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

About the Author :
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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Product Details
  • ISBN-13: 9780470633496
  • Publisher: John Wiley & Sons Inc
  • Publisher Imprint: John Wiley & Sons Inc
  • Height: 234 mm
  • No of Pages: 560
  • Returnable: N
  • Weight: 771 gr
  • ISBN-10: 0470633492
  • Publisher Date: 20 Feb 2012
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Spine Width: 36 mm
  • Width: 155 mm


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