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