Optimal, Predictive and Adaptive Control

OPTIMAL, PREDICTIVE,AND ADAPTIVE CONTRO L......Page 1
CONTENTS......Page 3
List of Figures......Page 7
1.1 Optimal, Predictive and Adaptive Control......Page 11
1.2 About This Book......Page 12
1.3 Part and Chapter Outline......Page 14
PART I BASIC DETERMINISTIC THEORY OF LQ AND PREDICTIVE CONTROL......Page 17
2.1 The Deterministic LQ Regulation Problem......Page 19
2.2 Dynamic Programming......Page 21
2.3 Riccati–Based Solution......Page 25
2.4 Time–Invariant LQR......Page 27
2.5 Steady–State LQR Computation......Page 39
2.6 Cheap Control......Page 42
2.7 Single Step Regulation......Page 46
Notes and References......Page 48
3.1 Sequences and Matrix Fraction Descriptions......Page 49
3.2 Feedback Systems......Page 55
3.3 Robust Stability......Page 63
3.4 Streamlined Notations......Page 66
3.5 1–DOF Trackers......Page 67
Notes and References......Page 70
CHAPTER 4 DETERMINISTIC LQ REGULATION – II......Page 71
4.1 Polynomial Formulation......Page 72
4.2 Causal–Anticausal Decomposition......Page 75
4.3 Stability......Page 76
4.4 Solvability......Page 79
4.5 Relationship with the Riccati–Based Solution......Page 82
4.6 Robust Stability of LQ Regulated Systems......Page 84
Notes and References......Page 86
5.1 Receding Horizon Regulation......Page 87
5.2 RDE Monotonicity and Stabilizing RHR......Page 90
5.3 Zero Terminal State RHR......Page 92
5.4 Stabilizing Dynamic RHR......Page 101
5.5 SIORHR Computations......Page 105
5.6 Generalized Predictive Regulation......Page 109
5.7 Receding Horizon Iterations......Page 113
5.8 Tracking......Page 124
Notes and References......Page 135
PART I I STATE ESTIMATION, SYSTEM IDENTIFICATION, LQ AND PREDICTIVE STOCHASTIC CONTROL......Page 137
6.1 Indirect Sensing Measurement Problems......Page 139
6.2 Kalman Filtering......Page 146
6.3 System Parameter Estimation......Page 158
6.4 Convergence of Recursive Identificatio Algorithms......Page 182
Notes and References......Page 195
7.1 LQ Stochastic Regulation: Complete State Information......Page 197
7.2 LQ Stochastic Regulation: Partial State Information......Page 202
7.3 Steady–State Regulation of CARMA Plants: Solution via Polynomial Equations......Page 209
7.4 Monotonic Performance Properties of LQ Stochastic Regulation......Page 223
7.5 Steady–State LQS Tracking and Servo......Page 225
and LQ Stochastic Control......Page 232
7.7 Predictive Control of CARMA Plants......Page 235
Notes and References......Page 241
PART III ADAPTIVE CONTROL......Page 243
CHAPTER 8 SINGLE–STEP–AHEAD SELF–TUNING CONTROL......Page 245
8.1 Control of Uncertain Plants......Page 246
8.2 Bayesian and Self–Tuning Control......Page 250
8.3 Global Convergence Tools for Deterministic STCs......Page 254
8.4 RLS Deterministic Properties......Page 258
8.5 Self–Tuning Cheap Control......Page 261
8.6 Constant Trace Normalized RLS and STCC......Page 267
8.7 Self–Tuning Minimum Variance Control......Page 272
8.8 Generalized Minimum–Variance Self–Tuning Control......Page 281
8.9 Robust Self–Tuning Cheap Control......Page 283
Notes and References......Page 291
9.1 Indirect Adaptive Predictive Control......Page 295
9.2 Implicit Multistep Prediction Models of Linear–Regression Type......Page 315
9.3 Use of Implicit Prediction Models in Adaptive Predictive Control......Page 319
9.4 MUSMAR as an Adaptive Reduced–Complexity Controller......Page 327
9.5 MUSMAR Local Convergence Properties......Page 338
9.6 Extensions of the MUSMAR Algorithm......Page 356
Notes and References......Page 374
A.1 State–Space Representations......Page 379
A.2 Stability......Page 382
A.3 State–Space Realizations......Page 383
B.1 Matrix–Fraction Descriptions......Page 385
B.2 Column– and Row–Reduced Matrices......Page 388
B.3 Reachable Realizations from Right MFDs......Page 389
B.5 Divisors and System–Theoretic Properties PBH rank tests......Page 390
C.1 Unilateral Polynomial Matrix Equations......Page 393
C.2 Bilateral Polynomial Matrix Equations......Page 395
D.2 Random Variables......Page 397
D.3 Conditional Probabilities......Page 399
D.5 Stochastic Processes......Page 400
D.6 Convergence......Page 401
D.7 Minimum Mean–Square–Error Estimators......Page 403