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<b>PREFACE xi</b> <p><b>1 STATIC OPTIMIZATION 1</b></p> <p>1.1 Optimization without Constraints / 1</p> <p>1.2 Optimization with Equality Constraints / 4</p> <p>1.3 Numerical Solution Methods / 15</p> <p>Problems / 15</p> <p><b>2 OPTIMAL CONTROL OF DISCRETE-TIME SYSTEMS 19</b></p> <p>2.1 Solution of the General Discrete-Time Optimization Problem / 19</p> <p>2.2 Discrete-Time Linear Quadratic Regulator / 32</p> <p>2.3 Digital Control of Continuous-Time Systems / 53</p> <p>2.4 Steady-State Closed-Loop Control and Suboptimal Feedback / 65</p> <p>2.5 Frequency-Domain Results / 96</p> <p>Problems / 102</p> <p><b>3 OPTIMAL CONTROL OF CONTINUOUS-TIME SYSTEMS 110</b></p> <p>3.1 The Calculus of Variations / 110</p> <p>3.2 Solution of the General Continuous-Time Optimization Problem / 112</p> <p>3.3 Continuous-Time Linear Quadratic Regulator / 135</p> <p>3.4 Steady-State Closed-Loop Control and Suboptimal Feedback / 154</p> <p>3.5 Frequency-Domain Results / 164</p> <p>Problems / 167</p> <p><b>4 THE TRACKING PROBLEM AND OTHER LQR EXTENSIONS 177</b></p> <p>4.1 The Tracking Problem / 177</p> <p>4.2 Regulator with Function of Final State Fixed / 183</p> <p>4.3 Second-Order Variations in the Performance Index / 185</p> <p>4.4 The Discrete-Time Tracking Problem / 190</p> <p>4.5 Discrete Regulator with Function of Final State Fixed / 199</p> <p>4.6 Discrete Second-Order Variations in the Performance Index / 206</p> <p>Problems / 211</p> <p><b>5 FINAL-TIME-FREE AND CONSTRAINED INPUT CONTROL 213</b></p> <p>5.1 Final-Time-Free Problems / 213</p> <p>5.2 Constrained Input Problems / 232</p> <p>Problems / 257</p> <p><b>6 DYNAMIC PROGRAMMING 260</b></p> <p>6.1 Bellman’s Principle of Optimality / 260</p> <p>6.2 Discrete-Time Systems / 263</p> <p>6.3 Continuous-Time Systems / 271</p> <p>Problems / 283</p> <p><b>7 OPTIMAL CONTROL FOR POLYNOMIAL SYSTEMS 287</b></p> <p>7.1 Discrete Linear Quadratic Regulator / 287</p> <p>7.2 Digital Control of Continuous-Time Systems / 292</p> <p>Problems / 295</p> <p><b>8 OUTPUT FEEDBACK AND STRUCTURED CONTROL 297</b></p> <p>8.1 Linear Quadratic Regulator with Output Feedback / 297</p> <p>8.2 Tracking a Reference Input / 313</p> <p>8.3 Tracking by Regulator Redesign / 327</p> <p>8.4 Command-Generator Tracker / 331</p> <p>8.5 Explicit Model-Following Design / 338</p> <p>8.6 Output Feedback in Game Theory and Decentralized Control / 343</p> <p>Problems / 351</p> <p><b>9 ROBUSTNESS AND MULTIVARIABLE FREQUENCY-DOMAIN TECHNIQUES 355</b></p> <p>9.1 Introduction / 355</p> <p>9.2 Multivariable Frequency-Domain Analysis / 357</p> <p>9.3 Robust Output-Feedback Design / 380</p> <p>9.4 Observers and the Kalman Filter / 383</p> <p>9.5 LQG/Loop-Transfer Recovery / 408</p> <p>9.6 <i>H</i>∞ DESIGN / 430</p> <p>Problems / 435</p> <p><b>10 DIFFERENTIAL GAMES 438</b></p> <p>10.1 Optimal Control Derived Using Pontryagin’s Minimum Principle and the Bellman Equation / 439</p> <p>10.2 Two-player Zero-sum Games / 444</p> <p>10.3 Application of Zero-sum Games to <i>H</i>∞ Control / 450</p> <p>10.4 Multiplayer Non-zero-sum Games / 453</p> <p><b>11 REINFORCEMENT LEARNING AND OPTIMAL ADAPTIVE CONTROL 461</b></p> <p>11.1 Reinforcement Learning / 462</p> <p>11.2 Markov Decision Processes / 464</p> <p>11.3 Policy Evaluation and Policy Improvement / 474</p> <p>11.4 Temporal Difference Learning and Optimal Adaptive Control / 489</p> <p>11.5 Optimal Adaptive Control for Discrete-time Systems / 490</p> <p>11.6 Integral Reinforcement Learning for Optimal Adaptive Control of Continuous-time Systems / 503</p> <p>11.7 Synchronous Optimal Adaptive Control for Continuous-time Systems / 513</p> <p><b>APPENDIX A REVIEW OF MATRIX ALGEBRA 518</b></p> <p>A.1 Basic Definitions and Facts / 518</p> <p>A.2 Partitioned Matrices / 519</p> <p>A.3 Quadratic Forms and Definiteness / 521</p> <p>A.4 Matrix Calculus / 523</p> <p>A.5 The Generalized Eigenvalue Problem / 525</p> <p><b>REFERENCES 527</b></p> <p><b>INDEX 535</b></p>

<p><b>FRANK L. LEWIS</b> 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. <p><b>DRAGUNA L. VRABIE</b> 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. <p><b>VASSILIS L. SYRMOS</b> 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.

<p><b>A NEW EDITION OF THE CLASSIC TEXT ON OPTIMAL CONTROL THEORY</b> <p>As a superb introductory text and an indispensable reference, this new edition of <i>Optimal Control</i> 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: <ul> <li>Static Optimization</li> <li>Optimal Control of Discrete-Time Systems</li> <li>Optimal Control of Continuous-Time Systems</li> <li>The Tracking Problem and Other LQR Extensions</li> <li>Final-Time-Free and Constrained Input Control</li> <li>Dynamic Programming</li> <li>Optimal Control for Polynomial Systems</li> <li>Output Feedback and Structured Control</li> <li>Robustness and Multivariable Frequency-Domain Techniques</li> <li>Differential Games</li> <li>Reinforcement Learning and Optimal Adaptive Control</li> </ul>

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