A unified computational approach to optimal control problems:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Harlow
Longman u.a.
1991
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
55 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 329 S. |
| ISBN: | 0582078105 |
Staff View
MARC
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| 245 | 1 | 0 | |a A unified computational approach to optimal control problems |c K. L. Teo ; C. J. Goh ; K. H. Wong |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow |b Longman u.a. |c 1991 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
A Note On Notation ix
1 Introduction 1
1.1 Preliminary 1
1.2 Some Basic Notions 1
1.3 Illustrative Examples 3
1.4 Some Further Notions 13
1.5 Historical Perspective 14
1.6 An Overview of Computational Algorithms 19
2 Mathematical Background 22
2.1 Introduction 22
2.2 Linear Vector Space 22
2.3 Topological Space 24
2.4 Metric Space 25
2.5 Normed Space 26
2.6 Elements in Measure Theory 29
2.7 Linear Functionals and Dual Spaces 32
2.8 Properties of Lp Spaces 35
2.9 Bounded Variation 37
3 Elements of Constrained Mathematical Programming ... 39
3.1 Introduction 39
3.2 Quadratic Programming with Linear Equality Constraints . . 42
3.3 Quadratic Programming via Active Set Strategy .... 46
3.4 Constrained Quasi Newton Method 51
3.5 Multiplier Penalty Function 53
3.6 The Sequential Quadratic Programming Algorithm ... 56
ii CONTENTS
4 Elements of Optimal Control Theory 60
4.1 Introduction 60
4.2 First Order Necessary Condition Euler Lagrangian Equation . 60
4.3 The Linear Quadratic Theory 64
4.4 Constraint Consideration and Canonical Formulation ... 69
4.5 Pontryagin Minimum Principle 72
4.6 Singular Control 76
4.7 Time Optimal Control 82
4.8 The Bellman Dynamic Programming 87
4.9 Exercises 93
5 Optimal Parameter Selection Problems 99
5.1 Introduction 99
5.2 Systems without Time Lag 100
5.2.1 Gradient Formulae 102
5.2.2 A Unified Computational Approach .... 105
5.3 Optimal Control Problems with Variable Switching Times . 105
5.4 A More General Optimal Parameter Selection Problem . 112
5.5 System with Time Lag 116
5.5.1 Gradient Formulae 118
5.6 Exercises 122
6 Optimal Control Problems in Canonical Form .... 128
6.1 Introduction 128
6.2 Problem Statement 129
6.3 Approximate Problems 132
6.4 Four Preliminary Lemmas 135
6.5 Some Convergence Results 138
6.6 A Unified Computational Approach 140
6.7 Illustrative Examples 144
6.8 Combined Optimal Control and Optimal Parameter Selection
Problems 148
6.8.1 Model Transformation 152
6.8.2 Smoothness of Optimal Control 154
6.8.3 Illustrative Examples 155
6.9 Exercises 161
CONTENTS iii
7 Optimal Control Problems Involving Linear Systems ... 164
7.1 Introduction 164
7.2 Problem Statement 164
7.3 Control Parametrization 166
7.4 Some Convergence Results 167
7.5 An Illustrative Example 170
7.6 Problems with Linear Terminal Inequality Constraints . 173
7.6.1 Approximate Problems 174
7.6.2 Some Convergence Results 176
7.7 Exercises 178
8 Nonlinear Optimal Control Problems with Functional Inequality State
Constraints 182
8.1 Introduction 182
8.2 Problem Statement 183
8.3 Constraint Approximation 184
8.4 Control Parametrization 191
8.5 Some Convergence Results 195
8.6 Additional Terminal Equality Constraints .... 196
8.7 Illustrative Examples 201
8.8 Combined Optimal Control and Optimal Parameter Selection
Problems 203
8.8.1 Illustrative Examples 208
8.9 Exercises 211
9 Optimal Control Problems with Almost Smooth Controls . . 213
9.1 Introduction 213
9.2 Problem Statement 213
9.3 Model Transformation 216
9.4 Control Parametrization 218
9.5 Constraints Approximation 222
9.6 Some Convergence Results 224
9.7 Illustrative Examples 226
9.8 Exercises 234
10 Optimal Control with a Cost of Changing Control ... 235
10.1 Introduction 235
10.2 Problem Statement 236
10.3 Control Parametrization 240
iv CONTENTS
10.4 Smoothing the Cost Functional 246
10.5 Constraints Approximation 248
10.6 Some Convergence Results 249
10.7 Illustrative Examples 252
10.8 Exercises 257
11 Discrete Time Optimal Control Problems 259
11.1 Introduction 259
11.2 Problem Statement 259
11.3 Canonical Formulation, Control Parametrization,
and Gradient Formulae 261
11.4 Constraints Approximation 266
11.5 Convergence Analysis 268
11.6 Illustrative Examples 270
11.7 Exercises 275
12 Time Delayed Optimal Control Problems 278
12.1 Introduction 278
12.2 Problem Statement 278
12.3 Variational Formulae 281
12.4 Approximate Problems 285
12.5 Some Convergence Results 288
12.6 A Unified Computational Approach 289
12.7 Illustrative Examples 289
12.8 Exercises 293
Appendix Further Problems and Exercises 295
References 313
Index 327
|
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| author | Teo, Kok Lay 1946- Goh, C. J. Wong, K. H. |
| author_GND | (DE-588)136134068 |
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| author_sort | Teo, Kok Lay 1946- |
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| building | Verbundindex |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV004593536 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:14:45Z |
| institution | BVB |
| isbn | 0582078105 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002823937 |
| oclc_num | 231245927 |
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| physical | IX, 329 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Longman u.a. |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Teo, Kok Lay 1946- Verfasser (DE-588)136134068 aut A unified computational approach to optimal control problems K. L. Teo ; C. J. Goh ; K. H. Wong 1. publ. Harlow Longman u.a. 1991 IX, 329 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 55 Algorithmus (DE-588)4001183-5 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Regelungstheorie (DE-588)4122327-5 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Algorithmus (DE-588)4001183-5 s DE-604 Regelungstheorie (DE-588)4122327-5 s Goh, C. J. Verfasser aut Wong, K. H. Verfasser aut Pitman monographs and surveys in pure and applied mathematics 55 (DE-604)BV000022446 55 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002823937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teo, Kok Lay 1946- Goh, C. J. Wong, K. H. A unified computational approach to optimal control problems Pitman monographs and surveys in pure and applied mathematics Algorithmus (DE-588)4001183-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Regelungstheorie (DE-588)4122327-5 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4121428-6 (DE-588)4122327-5 |
| title | A unified computational approach to optimal control problems |
| title_auth | A unified computational approach to optimal control problems |
| title_exact_search | A unified computational approach to optimal control problems |
| title_full | A unified computational approach to optimal control problems K. L. Teo ; C. J. Goh ; K. H. Wong |
| title_fullStr | A unified computational approach to optimal control problems K. L. Teo ; C. J. Goh ; K. H. Wong |
| title_full_unstemmed | A unified computational approach to optimal control problems K. L. Teo ; C. J. Goh ; K. H. Wong |
| title_short | A unified computational approach to optimal control problems |
| title_sort | a unified computational approach to optimal control problems |
| topic | Algorithmus (DE-588)4001183-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Regelungstheorie (DE-588)4122327-5 gnd |
| topic_facet | Algorithmus Optimale Kontrolle Regelungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002823937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
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