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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 |
Table of Contents provided by Ingram. All Rights Reserved. |
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Numerous examples highlight this treatment of the useof linear quadratic Gaussian methods for control system design. It explores linear optimal control theory from an engineering viewpoint, with illustrations of practical applications. Key topics include loop-recovery techniques, frequency shaping, and controller reduction. 1990 edition.
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