Optimal control of distributed parameter systems:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York u.a.
North-Holland
1981
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002147626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 430 S. |
| ISBN: | 0444005595 |
Internformat
MARC
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| 100 | 1 | |a Ahmed, Nasir U. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Optimal control of distributed parameter systems |c N. U. Ahmed ; K. L. Teo |
| 264 | 1 | |a New York u.a. |b North-Holland |c 1981 | |
| 300 | |a XIII, 430 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Commande, théorie de la |2 ram | |
| 650 | 7 | |a Systèmes à paramètres répartis |2 ram | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Distributed parameter systems | |
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| 700 | 1 | |a Teo, Kok Lay |d 1946- |e Verfasser |0 (DE-588)136134068 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819318021169086464 |
|---|---|
| adam_text | CONTENTS
Preface
CHAPTER ONE. MATHEMATICAL BACKGROUND 1
1.1. Elements of Functional Analysis 1
1.2. Special Function Spaces 17
1.3. Some Elements of Semigroup Theory 30
1.4. Measurable Set Valued Functions 37
CHAPTER TWO. PARTIAL DIFFERENTIAL EQUATIONS,
INTEGRAL EQUATIONS, AND EVOLUTION
EQUATIONS 41
2.1. First Boundary Value Problems for Parabolic
Partial Differential Equations in General Form 41
2.2. First Boundary Value Problems for Parabolic
Partial Differential Equations in Divergence Form 53
2.3. A Class of Volterra Integral Equations 92
2.4. Semigroup Approach to a Class of Linear
Evolution Equations 96
2.5. A Class of Nonlinear Evolution Equations 106
CHAPTER THREE. OPTIMAL CONTROL OF PARABOLIC
PARTIAL DIFFERENTIAL SYSTEMS WITH
CONTROLS IN THE COEFFICIENTS 121
3.1. First Boundary Value Problems
in General Form 122
3.1.1. Introduction 122
3.1.2. System Description 122
3.1.3. Existence and Uniqueness of Solutions 123
3.1.4. Formulation of Some Control Problems 123
3.1.5. Necessary Conditions for Optimality 125
3.1.6. Existence of Optimal Controls 138
viii CONTENTS
3 2. First Boundary Problems in Divergence Form 148
3.2.1. Introduction 148
3.2.2. System Description 149
3 2.3. Existence and Uniqueness of Weak Solutions 151
3 2.4. Formulation of Some Control Problems 153
3 2.5. Necessary Conditions for Optimality 155
3.2.6. Existence of Optimal Controls 172
3.3. Computational Methods 181
3.3.1. Introduction 181
3.3.2. Strong Variational Technique 182
3.3.3. Gradient Technique 190
3.4. Notes 194
CHAPTER FOUR OPTIMAL CONTROL OF HYPERBOLIC
PARTIAL DIFFERENTIAL SYSTEMS 200
4.1. First Order Hyperbolic Systems in One Spatial
Variable with Boundary Control 201
4.1.1. Introduction 201
4.1.2. System Description 201
4.1.3. Existence and Uniqueness of Solutions 203
4 14. Formulation of the Control Problem 209
4 1.5. Necessary and Sufficient Conditions for
Optimality 210
4 2. Second Order Hyperbolic Systems in One Spatial
Variable with Data from the Space of Distribution 214
4.2.1. Introduction 214
4.2.2. System Description 214
4.2.3. Existence and Uniqueness of Solutions 215
4.2.4. Formulation of the Control Problem 224
4 2 5. Necessary Conditions for Optimality 224
4.2.6. Existence of Optimal Controls 228
4.2.7. Computational Consideration 230
4 3. Second Order Hyperbolic Systems in One Spatial
Variable with Controls in the Coefficients 233
4.3.1. Introduction 233
4.3.2. System Description 233
4 3.3. Existence and Uniqueness of Solutions 234
4.3.4. Formulation of Some Control Problems 242
4.3.5. Necessary Conditions for Optimality 246
4.3.6. Existence of Optimal Controls 259
4.3.7. Computational Methods 268
4.4. Notes 271
CHAPTER FIVE OPTIMAL CONTROL OF EVOLUTION
EQUATIONS ON BANACH SPACES 275
5 1 Linear Evolution Equations in Coercive Form 275
5.1.1. Introduction 275
5.1.2. System Description 275
5.1.3. Existence and Uniqueness of Solutions 278
5.1.4. Formulation of Some Control Problems 283
5.1.5. Existence of Optimal Controls 284
CONTENTS ix
5.1.6. Necessary Conditions for Optimality 288
5.1.7. Optimal Feedback Control 295
5.2. Linear Evolution Equations Using Semigroup
Approach 319
5.2.1. Introduction 319
5.2.2. System Description 319
5.2.3. Existence and Uniqueness of Solutions 319
5.2.4. Formulation of Some Control Problems 320
5.2.5. Existence of Optimal Controls 321
5.2.6. Necessary Conditions for Optimality 329
5.2.7. Optimal Feedback Control 331
5.2.8. Time Optimal Control 339
5.3. Linear Evolution Equations Using Penalty
Function Approach 358
5.3.1. Introduction 358
5.3.2. System Description 359
5.3.3. Formulation of Some Control Problems 359
5.3.4. Existence of Optimal Controls and their
Approximation 360
5.3.5. An Example 367
5.4. A Class of Nonlinear Evolution Equations 368
5.4.1. Introduction 368
5.4.2. System Description 369
5.4.3. Existence and Uniqueness of Solutions 370
5.4.4. Formulation of Some Control Problems 371
5.4.5. Existence of Optimal Controls 372
5.4.6. Relaxed Systems 396
5.5. Notes 401
Bibliography 409
Index 426
|
| any_adam_object | 1 |
| author | Ahmed, Nasir U. Teo, Kok Lay 1946- |
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| author_facet | Ahmed, Nasir U. Teo, Kok Lay 1946- |
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV003397525 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:03:48Z |
| institution | BVB |
| isbn | 0444005595 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002147626 |
| oclc_num | 7553468 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-703 DE-739 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 DE-20 |
| physical | XIII, 430 S. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | North-Holland |
| record_format | marc |
| spellingShingle | Ahmed, Nasir U. Teo, Kok Lay 1946- Optimal control of distributed parameter systems Commande, théorie de la ram Systèmes à paramètres répartis ram Control theory Distributed parameter systems Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4032317-1 |
| title | Optimal control of distributed parameter systems |
| title_auth | Optimal control of distributed parameter systems |
| title_exact_search | Optimal control of distributed parameter systems |
| title_full | Optimal control of distributed parameter systems N. U. Ahmed ; K. L. Teo |
| title_fullStr | Optimal control of distributed parameter systems N. U. Ahmed ; K. L. Teo |
| title_full_unstemmed | Optimal control of distributed parameter systems N. U. Ahmed ; K. L. Teo |
| title_short | Optimal control of distributed parameter systems |
| title_sort | optimal control of distributed parameter systems |
| topic | Commande, théorie de la ram Systèmes à paramètres répartis ram Control theory Distributed parameter systems Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Commande, théorie de la Systèmes à paramètres répartis Control theory Distributed parameter systems Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002147626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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