Linear-Quadratic Control

by Dorato, Peter; Abdallah, Chaouki T.; Cerone, Vito

• ISBN13: 9780023299629
• ISBN10: 0023299622
• Edition: Facsimile
• Format: Hardcover
• Copyright: 1995-01-01
• Publisher: Prentice Hall

Summary

The purpose of this book is to provide an introduction to linear quadratic theory beyond the typical chapter on the subject found in texts on optimal or multivariable control. Of course, as an introductory text, the material here is not as detailed as that found in advanced books devoted exclusively to the subject.

Table of Contents

Preface	p. v
Table of Contents	p. vii
Forward	p. xi
Introduction	p. 1
Historical Sketch	p. 1
Prerequisites	p. 5
Organization and Scope of Text	p. 6
The LQR Problem	p. 9
LQR Problem Statement	p. 9
Hamilton-Jacobi Equation	p. 10
LQR Solution: Matrix Riccati Equation	p. 13
Riccati Equation Solution	p. 16
Steady-State Regulator Problem	p. 20
Sufficient Conditions for Optimality	p. 25
Selection of M, Q, and R Matrices	p. 28
Matlab Software	p. 31
Notes and References	p. 33
Problems	p. 36
Tracking and Disturbance Rejection	p. 43
Tracking Problem	p. 43
Disturbance-Rejection Problem	p. 44
Disturbance-Rejection Solution	p. 46
Steady-State and Preview Control	p. 50
Unknown Disturbances	p. 53
Matlab Software	p. 57
Notes and References	p. 60
Problems	p. 61
LQR Robustness Properties	p. 65
Robust-Stability Condition	p. 65
Kalman's Inequality	p. 68
Gain and Phase Margins	p. 74
Matlab Software	p. 75
Notes and References	p. 76
Problems	p. 77
Stochastic Control	p. 79
Stochastic Differential Equations	p. 80
Stochastic Hamilton-Jacobi Equation	p. 82
Additive Disturbances	p. 86
Multiplicative Disturbances	p. 89
Sufficient Conditions for Optimality	p. 93
Stochastic-Deterministic Dualism	p. 95
Matlab Software	p. 97
Notes and References	p. 99
Problems	p. 100
The LQG Problem	p. 103
Kalman-Bucy Filter	p. 103
LQG Solution: Separation Principle	p. 108
Fixed-Order Compensators	p. 113
Matlab Software	p. 118
Notes and References	p. 121
Problems	p. 123
Robustness Design	p. 129
The Robustness Problem	p. 129
LQG/LTR Design	p. 132
Guaranteed-Cost Design	p. 136
A Brief Survey of H[infinity] Methods	p. 145
Linear Matrix Inequality Methods	p. 157
Matlab Software	p. 160
Notes and References	p. 168
Problems	p. 171
Digital Control	p. 175
Digital-Control Issues	p. 176
Discrete-Time LQR Problem	p. 177
Discrete-Time LQR Optimization	p. 179
Steady-State Control	p. 181
Matlab Software	p. 184
Notes and References	p. 187
Problems	p. 188
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