Optimal control of ODEs and DAEs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
De Gruyter
2012
|
| Schriftenreihe: | De Gruyter graduate
De Gruyter textbook |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 458 S. graph. Darst. |
| ISBN: | 9783110249958 |
Internformat
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| 100 | 1 | |a Gerdts, Matthias |0 (DE-588)1013286952 |4 aut | |
| 245 | 1 | 0 | |a Optimal control of ODEs and DAEs |c Matthias Gerdts |
| 264 | 1 | |a Berlin [u.a.] |b De Gruyter |c 2012 | |
| 300 | |a IX, 458 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804143888487677952 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE INTRODUCTION 1
1.1 DAE OPTIMAL CONTROL PROBLEMS 8
1.1.1 PERTURBATION INDEX 24
1.1.2 CONSISTENT INITIAL VALUES 30
1.1.3 INDEX REDUCTION AND STABILIZATION 32
1.2 TRANSFORMATION TECHNIQUES 36
1.2.1 TRANSFORMATION TO FIXED TIME INTERVAL 36
1.2.2 TRANSFORMATION TO AUTONOMOUS PROBLEM 37
1.2.3 TRANSFORMATION OF TSCHEBYSCHEFF PROBLEMS 38
1.2.4 TRANSFORMATION OF L -MINIMIZATION PROBLEMS 38
1.2.5 TRANSFORMATION OF INTERIOR-POINT CONSTRAINTS 39
1.3 OVERVIEW 42
1.4 EXERCISES 44
INFINITE OPTIMIZATION PROBLEMS 50
2.1 FUNCTION SPACES 50
2.1.1 TOPOLOGICAL SPACES, BANACH SPACES, AND HILBERT SPACES . .. 51
2.1.2 MAPPINGS AND DUAL SPACES 54
2.1.3 DERIVATIVES, MEAN-VALUE THEOREM, AND IMPLICIT FUNCTION THEOREM 56
2.1.4 LP-SPACES, WG P -SPACES, ABSOLUTELY CONTINUOUS FUNCTIONS,
FUNCTIONS OF BOUNDED VARIATION 60
2.2 THE DAE OPTIMAL CONTROL PROBLEM AS AN INFINITE OPTIMIZATION PROBLEM
68
2.3 NECESSARY CONDITIONS FOR INFINITE OPTIMIZATION PROBLEMS 75 2.3.1
EXISTENCE OF A SOLUTION 77
2.3.2 CONIC APPROXIMATION OF SETS 79
2.3.3 SEPARATION THEOREMS 84
2.3.4 FIRST ORDER NECESSARY OPTIMALITY CONDITIONS OF FRITZ JOHN TYPE 87
2.3.5 CONSTRAINT QUALIFICATIONS AND KARUSH-KUHN-TUCKER CONDITIONS 95
2.4 EXERCISES 100
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1017753423
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
3 LOCAL MINIMUM PRINCIPLES 104
3.1 PROBLEMS WITHOUT PURE STATE AND MIXED CONTROL-STATE CONSTRAINTS . .
106 3.1.1 REPRESENTATION OF MULTIPLIERS I LL
3.1.2 LOCAL MINIMUM PRINCIPLE 114
3.1.3 CONSTRAINT QUALIFICATIONS AND REGULARITY 118
3.2 PROBLEMS WITH PURE STATE CONSTRAINTS 125
3.2.1 REPRESENTATION OF MULTIPLIERS 127
3.2.2 LOCAL MINIMUM PRINCIPLE 130
3.2.3 FINDING CONTROLS ON ACTIVE STATE CONSTRAINT ARCS 135
3.2.4 JUMP CONDITIONS FOR THE ADJOINT 137
3.3 PROBLEMS WITH MIXED CONTROL-STATE CONSTRAINTS 141
3.3.1 REPRESENTATION OF MULTIPLIERS 143
3.3.2 LOCAL MINIMUM PRINCIPLE 145
3.4 SUMMARY OF LOCAL MINIMUM PRINCIPLES FOR INDEX-ONE PROBLEMS . . . 148
3.5 EXERCISES 152
4 DISCRETIZATION METHODS FOR ODES AND DAES 157
4.1 DISCRETIZATION BY ONE-STEP METHODS 159
4.1.1 THE EULER METHOD 159
4.1.2 RUNGE-KUTTA METHODS 162
4.1.3 GENERAL ONE-STEP METHOD 168
4.1.4 CONSISTENCY, STABILITY, AND CONVERGENCE OF ONE-STEP METHODS 168
4.2 BACKWARD DIFFERENTIATION FORMULAS (BDF) 176
4.3 LINEARIZED IMPLICIT RUNGE-KUTTA METHODS 178
4.4 AUTOMATIC STEP-SIZE SELECTION 185
4.5 COMPUTATION OF CONSISTENT INITIAL VALUES 191
4.5.1 PROJECTION METHOD FOR CONSISTENT INITIAL VALUES 192
4.5.2 CONSISTENT INITIAL VALUES VIA RELAXATION 193
4.6 SHOOTING TECHNIQUES FOR BOUNDARY VALUE PROBLEMS 195
4.6.1 SINGLE SHOOTING METHOD USING PROJECTIONS 196
4.6.2 SINGLE SHOOTING METHOD USING RELAXATIONS 203
4.6.3 MULTIPLE SHOOTING METHOD 204
4.7 EXERCISES 208
5 DISCRETIZATION OF OPTIMAL CONTROL PROBLEMS 215
5.1 DIRECT DISCRETIZATION METHODS 216
5.1.1 FULL DISCRETIZATION APPROACH 218
5.1.2 REDUCED DISCRETIZATION APPROACH 220
5.1.3 CONTROL DISCRETIZATION 222
5.2 A BRIEF INTRODUCTION TO SEQUENTIAL QUADRATIC PROGRAMMING 227 5.2.1
LAGRANGE-NEWTON METHOD 227
5.2.2 SEQUENTIAL QUADRATIC PROGRAMMING (SQP) 229
IMAGE 3
CONTENTS IX
5.3 CALCULATION OF DERIVATIVES FOR REDUCED DISCRETIZATION 238
5.3.1 SENSITIVITY EQUATION APPROACH 239
5.3.2 ADJOINT EQUATION APPROACH: THE DISCRETE CASE 241
5.3.3 ADJOINT EQUATION APPROACH : THE CONTINUOUS CASE 248 5.4 DISCRETE
MINIMUM PRINCIPLE AND APPROXIMATION OF ADJOINTS 254 5.4.1 EXAMPLE 262
5.5 AN OVERVIEW ON CONVERGENCE RESULTS 273
5.5.1 CONVERGENCE OF THE EULER DISCRETIZATION 273
5.5.2 HIGHER ORDER OF CONVERGENCE FOR RUNGE-KUTTA DISCRETIZATIONS 276
5.6 NUMERICAL EXAMPLES 278
5.7 EXERCISES 288
6 REAL-TIME CONTROL 292
6.1 PARAMETRIC SENSITIVITY ANALYSIS AND OPEN-LOOP REAL-TIME CONTROL. .
293 6.1.1 PARAMETRIC SENSITIVITY ANALYSIS OF NONLINEAR OPTIMIZATION
PROBLEMS 293
6.1.2 OPEN-LOOP REAL-TIME CONTROL VIA SENSITIVITY ANALYSIS . . . . 303
6.2 FEEDBACK CONTROLLER DESIGN BY OPTIMAL CONTROL TECHNIQUES 315 6.3
MODEL PREDICTIVE CONTROL 325
6.4 EXERCISES 332
7 MIXED-INTEGER OPTIMAL CONTROL 338
7.1 GLOBAL MINIMUM PRINCIPLE 339
7.1.1 SINGULAR CONTROLS 351
7.2 VARIABLE TIME TRANSFORMATION METHOD 359
7.3 SWITCHING COSTS, DYNAMIC PROGRAMMING, BELLMAN S OPTIMALITY PRINCIPLE
373
7.3.1 DYNAMIC OPTIMIZATION MODEL WITH SWITCHING COSTS 374 7.3.2 A
DYNAMIC PROGRAMMING APPROACH 376
7.3.3 EXAMPLES 383
7.4 EXERCISES 391
8 FUNCTION SPACE METHODS 394
8.1 GRADIENT METHOD 395
8.2 LAGRANGE-NEWTON METHOD 411
8.2.1 COMPUTATION OF THE SEARCH DIRECTION 417
8.3 EXERCISES 429
BIBLIOGRAPHY 433
INDEX 455
|
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| ctrlnum | (OCoLC)711846769 (DE-599)BVBBV037266687 |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783110249958 |
| language | English |
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| spelling | Gerdts, Matthias (DE-588)1013286952 aut Optimal control of ODEs and DAEs Matthias Gerdts Berlin [u.a.] De Gruyter 2012 IX, 458 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate De Gruyter textbook System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-11-024999-6 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021179718&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gerdts, Matthias Optimal control of ODEs and DAEs System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4116671-1 (DE-588)4229517-8 (DE-588)4121428-6 |
| title | Optimal control of ODEs and DAEs |
| title_auth | Optimal control of ODEs and DAEs |
| title_exact_search | Optimal control of ODEs and DAEs |
| title_full | Optimal control of ODEs and DAEs Matthias Gerdts |
| title_fullStr | Optimal control of ODEs and DAEs Matthias Gerdts |
| title_full_unstemmed | Optimal control of ODEs and DAEs Matthias Gerdts |
| title_short | Optimal control of ODEs and DAEs |
| title_sort | optimal control of odes and daes |
| topic | System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | System von gewöhnlichen Differentialgleichungen Differential-algebraisches Gleichungssystem Optimale Kontrolle |
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