Infinite dimensional linear control systems: the time optimal and norm optimal problems
For more than forty years, the equation y'(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until re...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2005
|
| Edition: | 1. ed. |
| Series: | North-Holland mathematics studies
201 |
| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis |
| Summary: | For more than forty years, the equation y'(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y'(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 320 S. graph. Darst. |
| ISBN: | 0444516328 9780444516329 |
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| adam_text | Titel: Infinite dimensional linear control systems
Autor: Fattorini, Hector O
Jahr: 2005
CONTENTS
PREFACE vii
CHAPTER 1: INTRODUCTION
1.1. Finite dimensional systems: the maximum principle 1
1.2. Finite dimensional systems: existence and uniqueness 9
1.3. Infinite dimensional systems 16
CHAPTER 2: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, I
2.1. The reachable space and the bang-bang property 27
2.2. Reversible systems 36
2.3. The reachable space and its dual, I 47
2.4. The reachable space and its dual, II 56
2.5. The maximum principle 65
2.6. Vanishing of the costate and nonuniqueness in norm optimality 77
2.7. Vanishing of the costate for time optimal controls 87
2.8. Singular norm optimal controls 96
2.9. Singular norm optimal controls and singular functionals 108
CHAPTER 3: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, II
3.1. Existence and uniqueness of optimal controls 117
3.2. The weak maximum principle and the time optimal problem 125
3.3. Modeling of parabolic equations 134
3.4. Weakly singular extremals 143
3.5. More on the weak maximum principle 152
3.6. Convergence of minimizing sequences to optimal controls 163
CHAPTER 4: OPTIMAL CONTROL OF HEAT PROPAGATION
4.1. Modeling of parabolic equations 173
4.2. Adjoints 180
4.3. Adjoint semigroups 187
4.4. The reachable space 191
4.5. The reachable space and its dual. I 197
4.6. The reachable space and its dual, II 207
4.7. The maximum principle 215
4.8. Existence, uniqueness and stability of optimal controls 225
4.9. Examples and applications 231
xi
xii INFINITE DIMENSIONAL LINEAR CONTROL SYSTEMS
CHAPTER 5: OPTIMAL CONTROL OF DIFFUSIONS
5.1. Modeling of parabolic equations 243
5.2. The reachable space and its dual, I 252
5.3. The reachable space and its dual, II 258
5.4. The maximum principle 266
5.5. Existence of optimal controls; uniqueness and stability of supports 273
5.6. Examples and applications 285
CHAPTER 6: APPENDIX
6.1. Self adjoint operators, I 295
6.2. Self adjoint operators, II 301
6.3. Related research 305
REFERENCES 309
NOTATION AND SUBJECT INDEX 319
|
| adam_txt |
Titel: Infinite dimensional linear control systems
Autor: Fattorini, Hector O
Jahr: 2005
CONTENTS
PREFACE vii
CHAPTER 1: INTRODUCTION
1.1. Finite dimensional systems: the maximum principle 1
1.2. Finite dimensional systems: existence and uniqueness 9
1.3. Infinite dimensional systems 16
CHAPTER 2: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, I
2.1. The reachable space and the bang-bang property 27
2.2. Reversible systems 36
2.3. The reachable space and its dual, I 47
2.4. The reachable space and its dual, II 56
2.5. The maximum principle 65
2.6. Vanishing of the costate and nonuniqueness in norm optimality 77
2.7. Vanishing of the costate for time optimal controls 87
2.8. Singular norm optimal controls 96
2.9. Singular norm optimal controls and singular functionals 108
CHAPTER 3: SYSTEMS WITH STRONGLY MEASURABLE CONTROLS, II
3.1. Existence and uniqueness of optimal controls 117
3.2. The weak maximum principle and the time optimal problem 125
3.3. Modeling of parabolic equations 134
3.4. Weakly singular extremals 143
3.5. More on the weak maximum principle 152
3.6. Convergence of minimizing sequences to optimal controls 163
CHAPTER 4: OPTIMAL CONTROL OF HEAT PROPAGATION
4.1. Modeling of parabolic equations 173
4.2. Adjoints 180
4.3. Adjoint semigroups 187
4.4. The reachable space 191
4.5. The reachable space and its dual. I 197
4.6. The reachable space and its dual, II 207
4.7. The maximum principle 215
4.8. Existence, uniqueness and stability of optimal controls 225
4.9. Examples and applications 231
xi
xii INFINITE DIMENSIONAL LINEAR CONTROL SYSTEMS
CHAPTER 5: OPTIMAL CONTROL OF DIFFUSIONS
5.1. Modeling of parabolic equations 243
5.2. The reachable space and its dual, I 252
5.3. The reachable space and its dual, II 258
5.4. The maximum principle 266
5.5. Existence of optimal controls; uniqueness and stability of supports 273
5.6. Examples and applications 285
CHAPTER 6: APPENDIX
6.1. Self adjoint operators, I 295
6.2. Self adjoint operators, II 301
6.3. Related research 305
REFERENCES 309
NOTATION AND SUBJECT INDEX 319 |
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| spelling | Fattorini, Hector O. Verfasser aut Infinite dimensional linear control systems the time optimal and norm optimal problems H.O. Fattorini 1. ed. Amsterdam [u.a.] Elsevier 2005 XII, 320 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematics studies 201 Includes bibliographical references and index For more than forty years, the equation y'(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y'(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Control theory Calculus of variations Linear control systems Mathematical optimization Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Lineares Gleichungssystem (DE-588)4035826-4 s Optimierung (DE-588)4043664-0 s North-Holland mathematics studies 201 (DE-604)BV000003247 201 http://catdir.loc.gov/catdir/enhancements/fy0726/2005049489-d.html Beschreibung für Leser HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014663185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fattorini, Hector O. Infinite dimensional linear control systems the time optimal and norm optimal problems North-Holland mathematics studies Control theory Calculus of variations Linear control systems Mathematical optimization Variationsrechnung (DE-588)4062355-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4032317-1 (DE-588)4035826-4 (DE-588)4043664-0 |
| title | Infinite dimensional linear control systems the time optimal and norm optimal problems |
| title_auth | Infinite dimensional linear control systems the time optimal and norm optimal problems |
| title_exact_search | Infinite dimensional linear control systems the time optimal and norm optimal problems |
| title_exact_search_txtP | Infinite dimensional linear control systems the time optimal and norm optimal problems |
| title_full | Infinite dimensional linear control systems the time optimal and norm optimal problems H.O. Fattorini |
| title_fullStr | Infinite dimensional linear control systems the time optimal and norm optimal problems H.O. Fattorini |
| title_full_unstemmed | Infinite dimensional linear control systems the time optimal and norm optimal problems H.O. Fattorini |
| title_short | Infinite dimensional linear control systems |
| title_sort | infinite dimensional linear control systems the time optimal and norm optimal problems |
| title_sub | the time optimal and norm optimal problems |
| topic | Control theory Calculus of variations Linear control systems Mathematical optimization Variationsrechnung (DE-588)4062355-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Control theory Calculus of variations Linear control systems Mathematical optimization Variationsrechnung Kontrolltheorie Lineares Gleichungssystem Optimierung |
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