Optimal control theory for infinite dimensional systems
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston u.a.
Birkhäuser
1995
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| Schriftenreihe: | Systems & control
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Optimal control theory for infinite dimensional systems |c Xunjing Li ; Jiongmin Yong |
| 264 | 1 | |a Boston u.a. |b Birkhäuser |c 1995 | |
| 300 | |a XII, 448 S. | ||
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Datensatz im Suchindex
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|---|---|
| DE-BY-TUM_katkey | 652527 |
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| adam_text | XUNJING LI JIONGMIN YONG OPTIMAL CONTROL THEORY FOR INFINITE DIMENSIONAL
SYSTEMS BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE IX CHAPTER
1. CONTROL PROBLEMS IN INFINITE DIMENSIONS 1 §1. DIFFUSION PROBLEMS 1
§2. VIBRATION PROBLEMS 5 §3. POPULATION DYNAMICS 8 §4. FLUID DYNAMICS 12
§5. FREE BOUNDARY PROBLEMS 15 REMARKS 22 CHAPTER 2. MATHEMATICAL
PRELIMINARIES 24 §1. ELEMENTS IN FUNCTIONAL ANALYSIS 24 §1.1. SPACES 24
§1.2. LINEAR OPERATORS 27 §1.3. LINEAR FUNCTIONAL AND DUAL SPACES 28
§1.4. ADJOINT OPERATORS 31 §1.5. SPECTRAL THEORY 32 §1:6. COMPACT
OPERATORS 33 §2. SOME GEOMETRIC ASPECTS OF BANACH SPACES 36 §2.1. CONVEX
SETS 36 §2.2. CONVEXITY OF BANACH SPACES 41 §3. BANACH SPACE VALUED
FUNCTIONS 45 §3.1. MEASURABILITY AND INTEGRABILITY 45 §3.2. CONTINUITY
AND DIFFERENTIABILITY 47 §4. THEORY OF C O SEMIGROUPS 49 §4.1. UNBOUNDED
OPERATORS 49 §4.2. CO SEMIGROUPS 52 §4.3. SPECIAL TYPES OF CO SEMIGROUPS
55 §4.4. EXAMPLES 57 §5. EVOLUTION EQUATIONS 63 §5.1. SOLUTIONS 63 §5.2.
SEMILINEAR EQUATIONS 66 §5.3. VARIATION OF CONSTANTS FORMULA 68 §6.
ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS 71 §6.1. SOBOLEV SPACES 71 §6.2.
LINEAR ELLIPTIC EQUATIONS 75 §6.3. SEMILINEAR ELLIPTIC EQUATIONS 78
REMARKS 80 CHAPTER 3. EXISTENCE THEORY OF OPTIMAL CONTROLS 81 §1.
SOUSLIN SPACE 81 VI CONTENTS §1.1. POLISH SPACE 81 §1.2. SOUSLIN SPACE
84 §1.3. CAPACITY AND CAPACITABILITY 86 §2. MULTIFUNCTIONS AND SELECTION
THEOREMS 89 §2.1. CONTINUITY 89 §2.2. MEASURABILITY 94 §2.3. MEASURABLE
SELECTION THEOREMS 100 §3. EVOLUTION SYSTEMS WITH COMPACT SEMIGROUPS 109
§4. EXISTENCE OF FEASIBLE PAIRS AND OPTIMAL PAIRS 106 §4.1. CESARI
PROPERTY 106 §4.2. EXISTENCE THEOREMS 110 §5. SECOND ORDER EVOLUTION
SYSTEMS 113 §5.1. FORMULATION OF THE PROBLEM 113 §5.2. EXISTENCE OF
OPTIMAL CONTROLS 118 §6. ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS AND
VARIATIONAL INEQUALITIES 121 REMARKS 129 CHAPTER 4. NECESSARY CONDITIONS
FOR OPTIMAL CONTROLS * ABSTRACT EVOLUTION EQUATIONS 130 §1. FORMULATION
OF THE PROBLEM 130 §2. EKELAND VARIATIONAL PRINCIPLE 135 §3. OTHER
PRELIMINARY RESULTS 137 §3.1. FINITE CODIMENSIONALITY 137 §3.2.
PRELIMINARIES FOR SPIKE PERTURBATION 143 §3.3. THE DISTANCE FUNCTION 146
§4. PROOF OF THE MAXIMUM PRINCIPLE 150 §5. APPLICATIONS 159 REMARKS 165
CHAPTER 5. NECESSARY CONDITIONS FOR OPTIMAL CONTROLS * ELLIPTIC PARTIAL
DIFFERENTIAL EQUATIONS 168 §1. SEMILINEAR ELLIPTIC EQUATIONS 168 §1.1.
OPTIMAL CONTROL PROBLEM AND THE MAXIMUM PRINCIPLE 168 §1.2. THE STATE
CONSTRAINTS 171 §2. VARIATION ALONG FEASIBLE PAIRS 175 §3. PROOF OF THE
MAXIMUM PRINCIPLE 179 §4. VARIATIONAL INEQUALITIES 183 §4.1. STABILITY
OF THE OPTIMAL COST 184 §4.2. APPROXIMATE CONTROL PROBLEMS 185 §4.3.
MAXIMUM PRINCIPLE AND ITS PROOF 188 §5. QUASILINEAR EQUATIONS 191 §5.1.
THE STATE EQUATION AND THE OPTIMAL CONTROL PROBLEM 191 CONTENTS VII
§5.2. THE MAXIMUM PRINCIPLE 196 §6. MINIMAX CONTROL PROBLEM 197 §6.1.
STATEMENT OF THE PROBLEM 197 §6.2. REGULARIZATION OF THE COST FUNCTIONAL
199 §6.3. NECESSARY CONDITIONS FOR OPTIMAL CONTROLS 200 §7. BOUNDARY
CONTROL PROBLEMS 207 §7.1. FORMULATION OF THE PROBLEM 207 §7.2. STRONG
STABILITY AND THE QUALIFIED MAXIMUM PRINCIPLE 209 §7.3. NEUMANN PROBLEM
WITH MEASURE DATA 212 §7.4. EXACT PENALIZATION AND A PROOF OF THE
MAXIMUM PRINCIPLE 214 REMARKS 220 CHAPTER 6. DYNAMIC PROGRAMMING METHOD
FOR EVOLUTION SYSTEMS 223 §1. OPTIMALITY PRINCIPLE AND HAMILTON-JACOBI-
BELLMAN EQUATIONS 223 §2. PROPERTIES OF THE VALUE FUNCTIONS 227 §2.1.
CONTINUITY 228 §2.2. B-CONTINUITY 231 §2.3. SEMI-CONCAVITY 234 §3.
VISCOSITY SOLUTIONS 239 §4. UNIQUENESS OF VISCOSITY SOLUTIONS 244 §4.1.
A PERTURBED OPTIMIZATION LEMMA 244 §4.2. THE HILBERT SPACE X A 248 §4.3.
A UNIQUENESS THEOREM 250 §5. RELATION TO MAXIMUM PRINCIPLE AND OPTIMAL
SYNTHESIS 256 §6. INFINITE HORIZON PROBLEMS 264 REMARKS 272 CHAPTER 7.
CONTROLLABILITY AND TIME OPTIMAL CONTROL 274 §1. DEFINITIONS OF
CONTROLLABILITY 274 §2. CONTROLLABILITY FOR LINEAR SYSTEMS 278 §2.1.
APPROXIMATE CONTROLLABILITY 279 §2.2. EXACT CONTROLLABILITY 282 §3.
APPROXIMATE CONTROLLABILITY FOR SEMILINEAR SYSTEMS 286 §4. TIME OPTIMAL
CONTROL * SEMILINEAR SYSTEMS 294 §4.1. NECESSARY CONDITIONS FOR TIME
OPTIMAL PAIRS 294 §4.2. THE MINIMUM TIME FUNCTION 299 §5. TIME OPTIMAL
CONTROL * LINEAR SYSTEMS 302 §5.1. CONVEXITY OF THE REACHABLE SET 303
§5.2. ENCOUNTER OF MOVING SETS 308 §5.3. TIME OPTIMAL CONTROL 315
REMARKS 317 VIII CONTENTS CHAPTER 8. OPTIMAL SWITCHING AND IMPULSE
CONTROLS 319 §1. SWITCHING AND IMPULSE CONTROLS 319 §2. PRELIMINARY
RESULTS 322 §3. PROPERTIES OF THE VALUE FUNCTION 328 §4. OPTIMALITY
PRINCIPLE AND THE HJB EQUATION 331 §5. CONSTRUCTION OF AN OPTIMAL
CONTROL 334 §6. APPROXIMATION OF THE CONTROL PROBLEM 338 §7. VISCOSITY
SOLUTIONS 344 §8. PROBLEM IN FINITE HORIZON 352 REMARKS 359 CHAPTER 9.
LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS 361 §1. FORMULATION OF THE
PROBLEM 361 §1.1. EXAMPLES OF UNBOUNDED CONTROL PROBLEMS 361 §1.2. THE
LQ PROBLEM 366 §2. WELL-POSEDNESS AND SOLVABILITY 371 §3. STATE FEEDBACK
CONTROL 379 §3.1. TWO-POINT BOUNDARY VALUE PROBLEM 379 §3.2. THE PROBLEM
(LQ) T 382 §3.3. A FREDHOLM INTEGRAL EQUATION 386 §3.4. STATE FEEDBACK
REPRESENTATION OF OPTIMAL CONTROLS 391 §4. RICCATI INTEGRAL EQUATION 395
§5. PROBLEM IN INFINITE HORIZON 401 §5.1. REDUCTION OF THE PROBLEM 401
§5.2. WELL-POSEDNESS AND SOLVABILITY 405 §5.3. ALGEBRAIC RICCATI
EQUATION 407 §5.4. THE POSITIVE REAL LEMMA 408 §5.5. FEEDBACK
STABILIZATION 412 §5.6. FREDHOLM INTEGRAL EQUATION AND RICCATI INTEGRAL
EQUATION 414 REMARKS 415 REFERENCES 419 INDEX 443
|
| any_adam_object | 1 |
| author | Li, Xunjing Yong, Jiongmin 1958- |
| author_GND | (DE-588)121010481 |
| author_facet | Li, Xunjing Yong, Jiongmin 1958- |
| author_role | aut aut |
| author_sort | Li, Xunjing |
| author_variant | x l xl j y jy |
| building | Verbundindex |
| bvnumber | BV010163740 |
| classification_rvk | SK 880 |
| classification_tum | MAT 496f |
| ctrlnum | (OCoLC)246810963 (DE-599)BVBBV010163740 |
| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010163740 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T13:52:31Z |
| institution | BVB |
| isbn | 3764337222 0817637222 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006749743 |
| oclc_num | 246810963 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-12 DE-29T DE-634 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-12 DE-29T DE-634 DE-11 |
| physical | XII, 448 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Systems & control |
| spellingShingle | Li, Xunjing Yong, Jiongmin 1958- Optimal control theory for infinite dimensional systems Optimale Kontrolle (DE-588)4121428-6 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4207956-1 |
| title | Optimal control theory for infinite dimensional systems |
| title_auth | Optimal control theory for infinite dimensional systems |
| title_exact_search | Optimal control theory for infinite dimensional systems |
| title_full | Optimal control theory for infinite dimensional systems Xunjing Li ; Jiongmin Yong |
| title_fullStr | Optimal control theory for infinite dimensional systems Xunjing Li ; Jiongmin Yong |
| title_full_unstemmed | Optimal control theory for infinite dimensional systems Xunjing Li ; Jiongmin Yong |
| title_short | Optimal control theory for infinite dimensional systems |
| title_sort | optimal control theory for infinite dimensional systems |
| topic | Optimale Kontrolle (DE-588)4121428-6 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| topic_facet | Optimale Kontrolle Unendlichdimensionales System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006749743&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lixunjing optimalcontroltheoryforinfinitedimensionalsystems AT yongjiongmin optimalcontroltheoryforinfinitedimensionalsystems |