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培生经典书Adaptive Optimal Control_The Thinking Man's GPC.pdf
Contents
Preface
1 The Scene, the Props, the Players
1.1
Introduction and Purpose . . . . . . . . . . . . . . . . . . . .
1.2 A Jaundiced View of Adaptive Control History . . . . . . . .
1.3 Further Perspectives . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Robustness . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Recent Trends
. . . . . . . . . . . . . . . . . . . . . .
1.4 A Gedankenexample . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Open Loop Identification . . . . . . . . . . . . . . . .
1.4.2 Control Law Selection . . . . . . . . . . . . . . . . . .
1.4.3 Closed Loop Identification . . . . . . . . . . . . . . . .
1.4.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 The Audience . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 A Brief Tour
. . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Generalized Predictive Control
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 What is Predictive Control? . . . . . . . . . . . . . . .
2.1.3 A Brief Historical Perspective . . . . . . . . . . . . . .
2.2 The GPC Method of Clarke et al. . . . . . . . . . . . . . . . .
2.3 Optimal Prediction and GPC Solution . . . . . . . . . . . . .
2.4 A Simple GPC Example . . . . . . . . . . . . . . . . . . . . .
2.5 Closed Loop Formulae . . . . . . . . . . . . . . . . . . . . . .
2.6 GPC Based on a ‘Performance Model’
. . . . . . . . . . . . .
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
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Contents
3 Linear Quadratic Gaussian Optimal Control
3.1
3.2 The Linear Quadratic Regulator
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
3.2.1 The Finite Horizon Regulator . . . . . . . . . . . . . .
3.2.2 The Infinite Horizon Regulator . . . . . . . . . . . . .
3.2.3 The Receding Horizon Regulator . . . . . . . . . . . .
3.3 The Linear Quadratic Tracking Problem . . . . . . . . . . . .
3.4 The Linear Optimal State Estimator . . . . . . . . . . . . . .
3.4.1 The Kalman Predictor (KP)
. . . . . . . . . . . . . .
3.4.2 The Kalman Filter (KF) . . . . . . . . . . . . . . . . .
3.5 Optimal Filter Design with Disturbance Models . . . . . . . .
3.6 LQG Controllers . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 The Composite System and the LQ Objective . . . . .
3.6.2 Observers for the Composite System . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Examples
3.8 Closed Loop Control Formulae
. . . . . . . . . . . . . . . . .
3.9 GPC as LQG . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.1 Control Criterion Equivalence . . . . . . . . . . . . . .
3.9.2 An Example
. . . . . . . . . . . . . . . . . . . . . . .
3.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Stability and Performance Properties of Receding Horizon
83
83
85
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89
90
93
94
LQ Control
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Monotonicity and Stability of Receding Horizon LQ Control .
4.2.1
Stability via the ARE . . . . . . . . . . . . . . . . . .
4.2.2 Monotonicity Properties of the RDE . . . . . . . . . .
4.2.3
Stability via Monotonicity of the RDE . . . . . . . . .
4.3 Stabilizing Feedback Strategies . . . . . . . . . . . . . . . . .
4.3.1 Alternative Forms of the RDE . . . . . . . . . . . . .
4.3.2 The Stabilizing Controllers of Kwon, Pearson and Klein-
96
man . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
4.4 Mid Chapter Conclusion . . . . . . . . . . . . . . . . . . . . .
4.5 Comparative Performance of LQ Schemes . . . . . . . . . . .
98
4.6 Stability Properties of GPC . . . . . . . . . . . . . . . . . . . 101
4.6.1 An Unstable GPC Example . . . . . . . . . . . . . . . 102
4.6.2 Time-varying Strategies in Receding Horizon Control . 105
4.6.3 The Use of Nu in GPC Stability . . . . . . . . . . . . 106
4.6.4
Stability Theorems of Clarke and Mohtadi . . . . . . . 107
4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Contents
vii
5 Robust LQG Design — Features for Adaptive Control
5.1
113
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.1 A First Hint at the Adaptation/Robustness Interplay
114
5.1.2 A Guided Tour of LQG Robustness Theory . . . . . . 115
5.2 Robustness of Unity Feedback Systems . . . . . . . . . . . . . 117
5.3 LQ and KF Robustness — Return Difference Equalities
. . . 124
5.3.1 The LQ Return Difference Equality . . . . . . . . . . 124
5.3.2 The KP Return Difference Equality . . . . . . . . . . 127
5.3.3 The EDRs and LQ, KP Robustness
. . . . . . . . . . 127
5.4 Robustness of LQG Control — Loop Transfer Recovery . . . 130
5.4.1 Loop Transfer Recovery Rationale . . . . . . . . . . . 131
5.4.2 LQG Controller Transfer Functions . . . . . . . . . . . 132
5.4.3 The Discrete-time LTR Theory of Maciejowski
. . . . 135
5.5 An LQG/LTR Example . . . . . . . . . . . . . . . . . . . . . 141
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6 Recursive Least Squares Identification in Adaptive
Control
147
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2 Prediction Error Identification . . . . . . . . . . . . . . . . . 149
6.2.1 Off-line Prediction Error Identification: a Refresher
. 149
6.2.2 Recursive Least Squares Identification . . . . . . . . . 151
6.3 Frequency Domain Properties of the Identified Model . . . . . 153
6.3.1 Open Loop Identification . . . . . . . . . . . . . . . . 154
6.3.2 Closed Loop Identification . . . . . . . . . . . . . . . . 155
6.4 Recursive Identification in Closed Loop Control — Local
6.5 Recursive Identification in Closed Loop — Global Methods
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.4.1 Heuristic Motivation . . . . . . . . . . . . . . . . . . . 158
6.4.2 Potential Convergence Point
. . . . . . . . . . . . . . 160
Integral Manifolds and Slow Adaptation . . . . . . . . 164
6.4.3
. 168
6.5.1 Normalization and Deadzones . . . . . . . . . . . . . . 169
6.5.2 Projection and Leakage . . . . . . . . . . . . . . . . . 170
6.5.3 Covariance Resetting . . . . . . . . . . . . . . . . . . . 170
6.5.4 A Global Comment
. . . . . . . . . . . . . . . . . . . 171
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7 A Candidate Robust Adaptive Predictive Controller
175
7.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.2 The Certainty Equivalence Control Law . . . . . . . . . . . . 177
. . . . . . . . 177
7.2.1 The Plant, Noise and Reference Models
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Contents
7.2.2 Kalman Filter Design . . . . . . . . . . . . . . . . . . 179
7.2.3 LQ State-variable Feedback Design . . . . . . . . . . . 181
7.2.4 The LQG Controller . . . . . . . . . . . . . . . . . . . 182
7.3 The System Parameter Identifier . . . . . . . . . . . . . . . . 183
7.4 The Candidate — A Summary . . . . . . . . . . . . . . . . . 186
7.5 The Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
. . . . . . . . . . . . . . . 187
7.5.1 LQG Controller Properties
7.5.2 RLS Identifier Properties
. . . . . . . . . . . . . . . . 188
7.5.3 Manipulation of the Candidate Controller . . . . . . . 193
7.6 Computer Studies and Examples . . . . . . . . . . . . . . . . 194
7.6.1 The Gedankenexample Revisited . . . . . . . . . . . . 194
7.6.2 The Working Example Revisited . . . . . . . . . . . . 198
7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
8 Le Jugement Dernier
205
8.1
Introduction — The Final Analysis . . . . . . . . . . . . . . . 205
8.2 Adaptation and Stability Robustness . . . . . . . . . . . . . . 206
8.2.1 Linear Stability Robustness . . . . . . . . . . . . . . . 208
8.2.2 Closed Loop Identification and Stability Robustness . 212
8.3 Adaptation and Performance . . . . . . . . . . . . . . . . . . 215
8.4 Forethoughts on a Postscript
. . . . . . . . . . . . . . . . . . 217
8.5 Extensions and Generalizations . . . . . . . . . . . . . . . . . 220
8.5.1 Candidate Alternative Optimal Control Laws . . . . . 220
8.5.2 Alternative Identification Methods . . . . . . . . . . . 224
8.6 Refinements and Theoretical Support . . . . . . . . . . . . . . 226
8.6.1 Theoretical Refinements . . . . . . . . . . . . . . . . . 227
8.6.2 The Rohrs Examples . . . . . . . . . . . . . . . . . . . 228
8.6.3 Adaptive Control versus Robust Control . . . . . . . . 230
8.7 Coda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
References
Index
233
241
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