Foundations of deterministic and stochastic control:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
2002
|
| Series: | Systems & control
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 421 S. 24 cm |
| ISBN: | 3764342579 0817642579 |
Staff View
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Record in the Search Index
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| adam_text | IMAGE 1
JON H. DAVIS
FOUNDATIONS OF
DETERMINISTIC AND STOCHASTIC CONTROL
BIRKHAEUSER BOSTON * BASEL * BERLIN
IMAGE 2
CONTENTS
PREFACE VII
1 STATE SPACE REALIZATIONS 1
1.1 LINEAR MODELS 1
1.1.1 CONTINUOUS TIME 2
1.1.2 DISCRETETIME 4
1.2 REALIZATIONS 5
1.2.1 CONTROLLABILITY 6
1.2.2 CONTROLLABILITY AND REACHABILITY 9
1.2.3 OBSERVABILITY 11
1.2.4 MINIMAL REALIZATIONS 14
1.2.5 TIME INVARIANT PROBLEMS 22
1.3 CONSTRUCTING TIME INVARIANT REALIZATIONS 31
1.3.1 JORDAN FORM REALIZATIONS 32
1.3.2 MINIMALITY 36
1.3.3 COMPANION REALIZATIONS 37
1.3.4 STANDARD CONTROLLABLE REALIZATIONS 37
1.3.5 STANDARD OBSERVABLE REALIZATIONS 41
1.4 AN ACTIVE SUSPENSION MODEL 45
1.5 A MODEL IDENTIFICATION PROBLEM 49
1.5.1 MEASUREMENTS AND FILTERING 49
1.5.2 RECURSIVE LEAST SQUARES 51
1.5.3 IDENTIFYING A COUPLED EQUATION MODEL 54
1.5.4 COUPLED PROBLEM FORMULATION 55
IMAGE 3
X CONTENTS
1.6 SIMULATING RECURSIVE IDENTIFICATION 57
1.7 DISCRETE TIME MODELS 58
1.7.1 DISCRETE REALIZATIONS 60
1.7.2 DISCRETE TIME IDENTIFICATION 63
PROBLEMS 64
2 LEAST SQUARES CONTROL 71
2.1 MINIMUM ENERGY TRANSFERS 72
2.2 THE OUTPUT REGULATOR 74
2.2.1 FORM OFTHE OPTIMAL COST 74
2.2.2 COMPLETING THE SQUARE 76
2.2.3 RICCATI EQUATION EXISTENCE 79
2.2.4 ALGEBRAIC RICCATI EQUATION PROPERTIES 81
2.2.5 RICCATI SOLUTIONS AND CANONICAL EQUATIONS 84
2.2.6 DISCRETE TIME OUTPUT REGULATOR 87
2.2.7 STATIONARY RICCATI EQUATIONS 90
2.3 LINEAR REGULATOR TRACKING PROBLEMS 94
2.3.1 CONTINUOUS PROBLEM MODELS 95
2.3.2 THE CONTINUOUS OPTIMAL TRACKING CONTROL 95
2.3.3 DISCRETE TIME TRACKING MODEL 99
2.3.4 DISCRETE TIME OPTIMAL TRACKING CONTROL 99
2.4 DYNAMIC PROGRAMMING 102
PROBLEMS 105
3 STABILITY THEORY 109
3.1 INTRODUCTION 109
3.2 INTRODUCTION TO LYAPUNOV THEORY 109
3.3 DEFINITIONS 111
3.3.1 LYAPUNOV FUNCTIONS 111
3.3.2 NOTIONS OF STABILITY 113
3.4 CLASSICAL LYAPUNOV THEOREMS 116
3.4.1 TIME INVARIANT MODELS 119
3.4.2 PERTURBATION RESULTS 121
3.5 THE INVARIANCE APPROACH 123
3.5.1 DISCRETE TIME SYSTEMS 124
3.5.2 CONTINUOUS TIME MODELS 130
3.6 INPUT-OUTPUT STABILITY 132
3.6.1 FREQUENCY DOMAIN CRITERIA 132
3.6.2 VECTOR SPACES, NORMS, AND INPUT-OUTPUT MODELS 135
3.6.3 CONVOLUTION SYSTEMS: NYQUIST CRITERION 138
3.6.4 THE CIRCLE THEOREM 142
PROBLEMS 147
4 RANDOM VARIABLES AND PROCESSES 151
4.1 INTRODUCTION 151
IMAGE 4
CONTENTS XI
4.2 RANDOM VARIABLES 151
4.3 SAMPLE SPACES AND PROBABILITIES 153
4.4 DENSITIES 154
4.5 EXPECTATIONS, INNER PRODUCTS AND VARIANCES 154
4.5.1 NO DENSITIES? 156
4.6 LINEAR MINIMUM VARIANCE ESTIMATES 157
4.7 GRAMIANS AND COVARIANCE MATRICES 159
4.8 RANDOM PROCESSES 160
4.8.1 MEANS AND CORRELATIONS 162
4.8.2 VECTOR PROCESSES 163
4.8.3 STATIONARITY 165
4.8.4 LINEAR SYSTEMS 167
4.8.5 STATIONARY PROCESSES AND LTI FILTERS 170
4.9 GAUSSIAN VARIABLES 174
4.9.1 GAUSSIAN VECTORS 174
4.9.2 CONDITIONAL PROBABILITY 177
4.9.3 CONDITIONAL EXPECTATIONS 177
4.9.4 GAUSSIAN CONDITIONAL EXPECTATIONS 179
PROBLEMS 181
5 KALMAN-BUCY FILTERS 185
5.1 THE MODEL 185
5.2 ESTIMATION CRITERION 186
5.2.1 EASY NON-ANSWER 186
5.3 THE ONE STEP PREDICTOR 187
5.3.1 DERIVATION OF THE OPTIMAL FILTER 188
5.3.2 BOUNDEDNESS OF THE OPTIMAL FILTER 193
5.3.3 STABILITYOF THE OPTIMAL FILTER 195
PROBLEMS 198
6 CONTINUOUS TIME MODELS 201
6.1 INTRODUCTION 201
6.2 STOCHASTIC INTEGRALS 202
6.3 STOCHASTIC DIFFERENTIAL EQUATIONS 205
6.4 LINEAR MODELS 207
6.5 SECOND ORDER RESULTS 209
6.6 CONTINUOUS WHITE NOISE 212
6.7 CONTINUOUS TIME KALMAN-BUCY FILTERS 214
6.7.1 AN INTUITIVE DERIVATION 214
6.7.2 VERIFYING OPTIMALITY 217
6.7.3 EXAMPLES 223
PROBLEMS 226
7 THE SEPARATION THEOREM 229
7.1 STOCHASTIC DYNAMIC PROGRAMMING 229
IMAGE 5
XII CONTENTS
7.2 DYNAMIC PROGRAMMING ALGORITHM 231
7.3 DISCRETE TIME STOCHASTIC REGULATOR 232
7.3.1 FUELL STATE FEEDBACK 232
7.3.2 PARTIAL STATE OBSERVATIONS 234
7.3.3 SEPARATION THEOREM 237
7.4 CONTINUOUS TIME 239
7.5 THE TIME INVARIANT CASE 240
7.6 ACTIVE SUSPENSION 240
PROBLEMS 243
8 LUENBERGER OBSERVERS 245
8.1 FUELL STATE OBSERVERS 247
8.2 REDUCED ORDER OBSERVERS 249
PROBLEMS 253
9 NONLINEAR AND FINITE STATE PROBLEMS 255
9.1 INTRODUCTION 255
9.2 FINITE STATE MACHINES 256
9.2.1 GRAPHICAL REPRESENTATIONS 257
9.2.2 TRANSITION GRAPHS 257
9.2.3 BLOCK DIAGRAMS 258
9.2.4 TRELLIS DIAGRAMS 258
9.3 FINITE MARKOV PROCESSES 260
9.4 HIDDEN MARKOV MODELS 261
9.4.1 BCJR ALGORITHM 262
9.4.2 BCJR AND KAIMAN FILTERS 266
9.4.3 HIDDEN MARKOV MODEL SMOOTHING 266
9.4.4 COMPUTATIONAL REQUIREMENTS 267
PROBLEMS 268
10 WIENER-HOPF METHODS 271
10.1 WIENER FILTERS 271
10.2 SPECTRAL FACTORIZATION 273
10.3 THE SCALAR CASE - SPECTRAL FACTORIZATION 276
10.4 DISCRETE TIME FACTORIZATION 281
10.5 FACTORIZATION IN THE VECTOR CASE 283
10.5.1 CONTINUOUS TIME CASE 283
10.5.2 DISCRETE TIME VERSION 284
10.5.3 VARIANT DETAILS 285
10.6 FINITE DIMENSIONAL SYMMETRIE PROBLEMS 286
10.7 SPECTRAL FACTORS AND OPTIMAL GAINS 288
10.8 LINEAR REGULATORS AND THE PROJECTION THEOREM 291
PROBLEMS 295
11 DISTRIBUTED SYSTEM REGULATORS 297
IMAGE 6
CONTENTS XIII
11.1 OPEN LOOP UNSTABLE DISTRIBUTED REGULATORS 297
11.2 THE WIENER-HOPF CONDITION 302
11.3 OPTIMAL FEEDBACK GAINS 307
11.4 MATCHED FILTER EVASION 314
PROBLEMS 318
12 FILTERS WITHOUT RICCATI EQUATIONS 321
12.1 INTRODUCTION 321
12.2 BASIC PROBLEM FORMULATION 322
12.3 SPECTRAL FACTORS 324
12.4 CLOSED LOOP STABILITY 327
12.5 REALIZING THE OPTIMAL FILTER 330
PROBLEMS 331
13 NEWTON S METHOD FOR RICCATI EQUATIONS 333
13.1 NEWTON S METHOD 333
13.2 CONTINUOUS TIME RICCATI EQUATIONS 334
13.3 DISCRETE TIME RICCATI EQUATIONS 335
13.4 CONVERGENCE OF NEWTON S METHOD 337
13.4.1 CONTINUOUS TIME CONVERGENCE 337
13.4.2 DISCRETE TIME CONVERGENCE 340
14 NUMERICAL SPECTRAL FACTORIZATION 343
14.1 INTRODUCTION 343
14.2 AN INTUITIVE ALGORITHM DERIVATION 344
14.3 A CONVERGENCE PROOF FOR THE CONTINUOUS TIME ALGORITHM 346 14.4
IMPLEMENTATION 348
14.5 THE DISCRETE CASE 352
14.6 NUMERICAL COMMENTS 354
A HUBERT AND BANACH SPACES AND OPERATORS 357
A. 1 BANACH AND HUBERT SPACES 357
A.2 QUOTIENT SPACES 358
A.3 DUAL SPACES 359
A.4 BOUNDED LINEAR OPERATORS 361
A.5 INDUCEDNORMS 362
A.6 THE BANACH SPACE C(X, Y) 364
A.7 ADJOINT MAPPINGS 364
A.8 ORTHOGONAL COMPLEMENTS 365
A.9 PROJECTION THEOREM 366
A.10 ABSTRACT LINEAR EQUATIONS 369
A.LL LINEAR EQUATIONS AND ADJOINTS 371
A. 12 MINIMUM MISS DISTANCE PROBLEMS 373
A.13 MINIMUM NORM PROBLEMS 373
IMAGE 7
XIV CONTENTS
A.14 FREDHOLM OPERATORS 375
A.15 BANACH ALGEBRAS 379
A.15.1 INVERSES AND SPECTRA 382
A.15.2 IDEALS, TRANSFORMS, AND SPECTRA 385
A.15.3 FUNCTIONAL CALCULUS 395
B MEASURE THEORETIC PROBABILITY 399
B.L MEASURE THEORY 399
B.2 RANDOM VARIABLES 401
B.3 INTEGRALS AND EXPECTATION 402
B.4 DERIVATIVES AND DENSITIES 403
B.5 CONDITIONAL PROBABILITIES AND EXPECTATIONS 405
B.5.1 CONDITIONAL PROBABILITY 405
B.5.2 CONDITIONAL EXPECTATIONS 406
REFERENCES 411
INDEX 417
|
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| indexdate | 2024-07-09T19:03:43Z |
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| language | English |
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| publishDate | 2002 |
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| spelling | Davis, Jon H. 1943- Verfasser (DE-588)122720997 aut Foundations of deterministic and stochastic control Jon H. Davis Boston ; Basel ; Berlin Birkhäuser 2002 XIV, 421 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Systems & control Commande stochastique Commande, Théorie de la Control theory Stochastic control theory Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Lineare Kontrolltheorie (DE-588)4123657-9 gnd rswk-swf Lineare Kontrolltheorie (DE-588)4123657-9 s DE-604 Stochastische Kontrolltheorie (DE-588)4263657-7 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009906975&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davis, Jon H. 1943- Foundations of deterministic and stochastic control Commande stochastique Commande, Théorie de la Control theory Stochastic control theory Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Lineare Kontrolltheorie (DE-588)4123657-9 gnd |
| subject_GND | (DE-588)4263657-7 (DE-588)4123657-9 |
| title | Foundations of deterministic and stochastic control |
| title_auth | Foundations of deterministic and stochastic control |
| title_exact_search | Foundations of deterministic and stochastic control |
| title_full | Foundations of deterministic and stochastic control Jon H. Davis |
| title_fullStr | Foundations of deterministic and stochastic control Jon H. Davis |
| title_full_unstemmed | Foundations of deterministic and stochastic control Jon H. Davis |
| title_short | Foundations of deterministic and stochastic control |
| title_sort | foundations of deterministic and stochastic control |
| topic | Commande stochastique Commande, Théorie de la Control theory Stochastic control theory Stochastische Kontrolltheorie (DE-588)4263657-7 gnd Lineare Kontrolltheorie (DE-588)4123657-9 gnd |
| topic_facet | Commande stochastique Commande, Théorie de la Control theory Stochastic control theory Stochastische Kontrolltheorie Lineare Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009906975&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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