Optimal Control Linear Quadratic Methods

by Anderson, Brian D. O.; Moore, John B.

• ISBN13: 9780486457666
• ISBN10: 0486457664
• Format: Paperback
• Copyright: 2007-02-27
• Publisher: Dover Publications

Summary

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material. The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback.

Author Biography

Brian D. O. Anderson and John B. Moore are the authors of Dover's Optimal Filtering and are both on the faculty of The Australian National University, Canberra.

Table of Contents

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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