Optimal Control : Linear Quadratic Methods

Preface ix Part I. Basic Theory of the Optimal Regulator Introduction 1(6) Linear Optimal Control 1(3) About This Book in Particular 4(1) Part and Chapter Outline 5(2) The Standard Regulator Problem---I 7(28) A Review of the Regulator Problem 7(5) The Hamilton-Jacobi Equation 12(8) Solution of the Finite-Time Regulator Problem 20(8) Discrete Time Systems 28(7) The Standard Regulator Problem---II 35(33) The Infinite-Time Regulator Problem 35(10) Stability of the Time-Invariant Regulator 45(6) Summary and Discussion of the Regulator Problem Results 51(5) Cross-Product Terms and Second Variation Theory 56(4) Regulator with a Prescribed Degree of Stability 60(8) Tracking Systems 68(33) The Problem of Achieving a Desired Trajectory 68(3) Finite-Time Results 71(13) Infinite-Time Results 84(11) A Practical Design Example 95(6) Part II. Properties and Application of the Optimal Regulator Properties of Regulator Systems with a Classical Control Interpretation 101(38) The Regulator from an Engineering Viewpoint 101(3) Return Difference Equality and Related Formulas 104(6) Some Classical Control Ideas: Sensitivity, Complementary Sensitivity, and Robustness 110(6) Gain Margin, Phase Margin, and Time-Delay Tolerance 116(11) Insertion of Nonlinearities 127(4) The Inverse Optimal Control Problem 131(3) Return Difference Equality for Discrete-Time Regulators 134(5) Asymptotic Properties and Quadratic Weight Selection 139(25) Single Input Systems 139(9) Multivariable Systems 148(8) Further Issues in Q, R Selection 156(8) State Estimator Design 164(43) The Nature of the State Estimation Problem 164(4) Deterministic Estimator Design 168(10) Statistical Estimator Design (The Kalman-Bucy Filter) 178(29) System Design Using State Estimators 207(55) Controller Design---Basic Versions and Variations 207(11) The Separation Theorem and Performance Calculation 218(10) Loss of Passband Robustness with Observers 228(8) Loop Recovery 236(15) Robustness Improvement via Residual Feedback 251(11) Frequency Shaping 262(27) Blending Classical and Linear Quadratic Methods 262(6) State Estimate Feedback with Frequency Shaping 268(4) Proportional Plus Integral State Feedback 272(10) Proportional Plus Integral State Estimate Feedback 282(7) Controller Reduction 289(34) Introduction: Selection of Frequency Weighting 289(5) Frequency-Weighted Balanced Truncation 294(10) Approaches to Controller Reduction via Fractional Representations 304(13) Direct Design of Low-Order Controllers 317(6) Digital Controllers 323(13) Controller Implementation 323(2) Sampling Time Selection 325(3) Anti-Aliasing Analog Prefilter 328(2) The Discrete-Time Transfer Function 330(4) State-Variable Implementation of the Discrete-Time Transfer Function 334(2) Appendices 336(39) Appendix A Brief Review of Some Results of Matrix Theory 336(17) Appendix B Brief Review of Some Major Results of Linear System Theory 353(10) Appendix C The Pontryagin Minimum Principle and Linear Optimal Control 363(4) Appendix D Lyapunov Stability 367(3) Appendix E The Riccati Equation 370(5) Author Index 375(2) Subject Index 377(4) Solutions 381