Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1997
|
| Series: | Systems & control: Foundations & applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 570 S. graph. Darst. |
| ISBN: | 0817636404 3764336404 |
Staff View
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| adam_text | MARTINO BARDI ITALO CAPUZZO-DOLCETTA OPTIMAL CONTROL AND VISCOSITY
SOLUTIONS OF HAMILTON-JACOBI-BELLMAN EQUATIONS BIRKHAUSER BOSTON * BASEL
* BERLIN CONTENTS PREFACE XI BASIC NOTATIONS XV CHAPTER I. OUTLINE OF
THE MAIN IDEAS ON A MODEL PROBLEM 1 1. THE INFINITE HORIZON DISCOUNTED
REGULATOR 1 2. THE DYNAMIC PROGRAMMING PRINCIPLE 2 3. THE
HAMILTON-JACOBI-BELLMAN EQUATION IN THE VISCOSITY SENSE . . . . 3 4.
COMPARISON, UNIQUENESS AND STABILITY OF VISCOSITY SOLUTIONS 6 5.
SYNTHESIS OF OPTIMAL CONTROLS AND VERIFICATION THEOREMS 10 6. PONTRYAGIN
MAXIMUM PRINCIPLE AS A NECESSARY AND SUFFICIENT CONDITION OF OPTIMALITY
13 7. DISCRETE TIME DYNAMIC PROGRAMMING AND CONVERGENCE OF
APPROXIMATIONS 17 8. THE VISCOSITY APPROXIMATION AND STOCHASTIC CONTROL
20 9. BIBLIOGRAPHICAL NOTES 21 CHAPTER II. CONTINUOUS VISCOSITY
SOLUTIONS OF HAMILTON-JACOBI EQUATIONS 25 1. DEFINITIONS AND BASIC
PROPERTIES , 25 2. SOME CALCULUS AND FURTHER PROPERTIES OF VISCOSITY
SOLUTIONS 34 3. SOME COMPARISON AND UNIQUENESS RESULTS 50 4. LIPSCHITZ
CONTINUITY AND SEMICONCAVITY 61 4.1. LIPSCHITZ CONTINUITY 62 4.2.
SEMICONCAVITY 65 5. SPECIAL RESULTS FOR CONVEX HAMILTONIANS 77 5.1.
SEMICONCAVE GENERALIZED SOLUTIONS AND BILATERAL SUPERSOLUTIONS 77 5.2.
DIFFERENTIABILITY OF SOLUTIONS . . ._ 80 5.3. A COMPARISON THEOREM 82
5.4. SOLUTIONS IN THE EXTENDED SENSE 84 VI CONTENTS 5.5. DIFFERENTIAL
INEQUALITIES IN THE VISCOSITY SENSE 86 5.6. MONOTONICITY OF VALUE
FUNCTIONS ALONG TRAJECTORIES 90 6. BIBLIOGRAPHICAL NOTES 95 CHAPTER III.
OPTIMAL CONTROL PROBLEMS WITH CONTINUOUS VALUE FUNCTIONS: UNRESTRICTED
STATE SPACE 97 1. THE CONTROLLED DYNAMICAL SYSTEM 97 2. THE INFINITE
HORIZON PROBLEM 99 2.1. DYNAMIC PROGRAMMING AND THE
HAMILTON-JACOBI-BELLMAN EQUATION 99 2.2. SOME SIMPLE APPLICATIONS:
VERIFICATION THEOREMS, RELAXATION, STABILITY 110 2.3. BACKWARD DYNAMIC
PROGRAMMING, SUB- AND SUPEROPTIMALITY PRINCIPLES, BILATERAL SOLUTIONS
119 2.4. GENERALIZED DIRECTIONAL DERIVATIVES AND EQUIVALENT NOTIONS OF
SOLUTION 125 2.5. NECESSARY AND SUFFICIENT CONDITIONS OF OPTIMALITY,
MINIMUM PRINCIPLES, AND MULTIVALUED OPTIMAL FEEDBACKS 133 3. THE FINITE
HORIZON PROBLEM 147 3.1. THE HJB EQUATION 147 3.2. LOCAL COMPARISON AND
UNBOUNDED VALUE FUNCTIONS 156 3.3. EQUIVALENT NOTIONS OF SOLUTION 160
3.4. NECESSARY AND SUFFICIENT CONDITIONS OF OPTIMALITY AND THE
PONTRYAGIN MAXIMUM PRINCIPLE 170 4. PROBLEMS WHOSE HJB EQUATION IS A
VARIATIONAL OR QUASIVARIATIONAL INEQUALITY 183 4.1. THE MONOTONE CONTROL
PROBLEM 184 4.2. OPTIMAL STOPPING 193 4.3. IMPULSE CONTROL 200 4.4.
OPTIMAL SWITCHING 210 5. APPENDIX: SOME RESULTS ON ORDINARY DIFFERENTIAL
EQUATIONS 218 6. BIBLIOGRAPHICAL NOTES 223 CHAPTER IV. OPTIMAL CONTROL
PROBLEMS WITH CONTINUOUS VALUE FUNCTIONS: RESTRICTED STATE SPACE 227 1.
SMALL-TIME CONTROLLABILITY AND MINIMAL TIME FUNCTIONS 227 2. HJB
EQUATIONS AND BOUNDARY VALUE PROBLEMS FOR THE MINIMAL TIME FUNCTION:
BASIC THEORY 239 3. PROBLEMS WITH EXIT TIMES AND NON-ZERO TERMINAL COST
247 3.1. COMPATIBLE TERMINAL COST AND CONTINUITY OF THE VALUE FUNCTION
248 3.2. THE HJB EQUATION AND A SUPEROPTIMALITY PRINCIPLE 254 4. FREE
BOUNDARIES AND LOCAL COMPARISON RESULTS FOR UNDISCOUNTED PROBLEMS WITH
EXIT TIMES 261 5. PROBLEMS WITH STATE CONSTRAINTS 271 6. BIBLIOGRAPHICAL
NOTES 282 CONTENTS VII CHAPTER V. DISCONTINUOUS VISCOSITY SOLUTIONS AND
APPLICATIONS 285 1. SEMICONTINUOUS SUB- AND SUPERSOLUTIONS, WEAK LIMITS,
AND STABILITY . 286 2. NON-CONTINUOUS SOLUTIONS 295 2.1. DEFINITIONS,
BASIC PROPERTIES, AND EXAMPLES 295 2.2. EXISTENCE OF SOLUTIONS BY
PERRON S METHOD 302 3. ENVELOPE SOLUTIONS OF DIRICHLET PROBLEMS 308 3.1.
EXISTENCE AND UNIQUENESS OF E-SOLUTIONS 309 3.2. TIME-OPTIMAL PROBLEMS
LACKING CONTROLLABILITY 313 4. BOUNDARY CONDITIONS IN THE VISCOSITY
SENSE 316 4.1. MOTIVATIONS AND BASIC PROPERTIES 317 4.2. COMPARISON
RESULTS AND APPLICATIONS TO EXIT-TIME PROBLEMS AND STABILITY 326 4.3.
UNIQUENESS AND COMPLETE SOLUTION FOR TIME-OPTIMAL CONTROL . . 333 5.
BILATERAL SUPERSOLUTIONS 342 5.1. PROBLEMS WITH EXIT TIMES AND GENERAL
TARGETS 342 5.2. FINITE HORIZON PROBLEMS WITH CONSTRAINTS ON THE
ENDPOINT OF THE TRAJECTORIES * . 348 6. BIBLIOGRAPHICAL NOTES 357
CHAPTER VI. APPROXIMATION AND PERTURBATION PROBLEMS 359 1. SEMIDISCRETE
APPROXIMATION AND E-OPTIMAL FEEDBACKS 359 1.1. APPROXIMATION OF THE
VALUE FUNCTION AND CONSTRUCTION OF OPTIMAL CONTROLS 360 1.2. A FIRST
RESULT ON THE RATE OF CONVERGENCE 369 1.3. IMPROVING THE RATE OF
CONVERGENCE 372 2. REGULAR PERTURBATIONS 376 3. STOCHASTIC CONTROL WITH
SMALL NOISE AND VANISHING VISCOSITY 383 4. APPENDIX: DYNAMIC PROGRAMMING
FOR DISCRETE TIME SYSTEMS . . . 388 5. BIBLIOGRAPHICAL NOTES 395 CHAPTER
VII. ASYMPTOTIC PROBLEMS 397 1. ERGODIC PROBLEMS 397 1.1. VANISHING
DISCOUNT IN THE STATE CONSTRAINED PROBLEM 397 1.2. VANISHING DISCOUNT IN
THE UNCONSTRAINED CASE: OPTIMAL STOPPING 402 2. VANISHING SWITCHING
COSTS 411 3. PENALIZATION 414 3.1. PENALIZATION OF STOPPING COSTS 414
3.2. PENALIZATION OF STATE CONSTRAINTS 417 4. SINGULAR PERTURBATION
PROBLEMS 420 4.1. THE INFINITE HORIZON PROBLEM FOR SYSTEMS WITH FAST
COMPONENTS 420 4.2. ASYMPTOTICS FOR THE MONOTONE CONTROL PROBLEM 426 5.
BIBLIOGRAPHICAL NOTES 429 VIII CONTENTS CHAPTER VIII. DIFFERENTIAL GAMES
431 1. DYNAMIC PROGRAMMING FOR LOWER AND UPPER VALUES 433 2. EXISTENCE
OF A VALUE, RELAXATION, VERIFICATION THEOREMS 442 3. COMPARISON WITH
OTHER INFORMATION PATTERNS AND OTHER NOTIONS OF VALUE 448 3.1. FEEDBACK
STRATEGIES 448 3.2. APPROXIMATION BY DISCRETE TIME GAMES 457 4.
BIBLIOGRAPHICAL NOTES 468 APPENDIX A. NUMERICAL SOLUTION OF DYNAMIC
PROGRAMMING EQUATIONS BY MAURIZIO FALCONE 471 1. THE INFINITE HORIZON
PROBLEM 472 1.1. THE DYNAMIC PROGRAMMING EQUATION 473 1.2. SYNTHESIS OF
FEEDBACK CONTROLS 478 1.3. NUMERICAL TESTS 481 2. PROBLEMS WITH STATE
CONSTRAINTS 484 3. MINIMUM TIME PROBLEMS AND PURSUIT-EVASION GAMES . . .
Y ..... 488 3.1. TIME-OPTIMAL CONTROL 488 3.2. PURSUIT-EVASION GAMES
494 3.3. NUMERICAL TESTS 496 4. SOME HINTS FOR THE CONSTRUCTION OF THE
ALGORITHMS 499 5. BIBLIOGRAPHICAL NOTES 502 APPENDIX B. NONLINEAR HOO
CONTROL BY PIERPAOLO SORAVIA 505 1. DEFINITIONS 506 2. LINEAR SYSTEMS
510 3. WOO CONTROL AND DIFFERENTIAL GAMES 512 4. DYNAMIC PROGRAMMING
EQUATION 515 5. ON THE PARTIAL INFORMATION PROBLEM 521 6. SOLVING THE
PROBLEM 527 7. EXERCISES 530 8R BIBLIOGRAPHICAL NOTES 531 BIBLIOGRAPHY
533 INDEX 565
|
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| genre_facet | Dynamische Programmierung |
| id | DE-604.BV011705284 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:14:20Z |
| institution | BVB |
| isbn | 0817636404 3764336404 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007892899 |
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| physical | XVII, 570 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Systems & control: Foundations & applications |
| spelling | Bardi, Martino 1956- Verfasser (DE-588)115277463 aut Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations Martino Bardi ; Italo Capuzzo-Dolcetta Boston [u.a.] Birkhäuser 1997 XVII, 570 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Systems & control: Foundations & applications Commande, Théorie de la Commande, Théorie de la ram Jeux différentiels Jeux différentiels ram Solutions de viscosité Control theory Differential games Viscosity solutions Viskositätslösung (DE-588)4463279-4 gnd rswk-swf Differentialspiel (DE-588)4012253-0 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd rswk-swf Dynamische Programmierung gnd rswk-swf Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 s Optimale Kontrolle (DE-588)4121428-6 s Dynamische Programmierung f DE-604 Viskositätslösung (DE-588)4463279-4 s Differentialspiel (DE-588)4012253-0 s Capuzzo Dolcetta, Italo 1948- Verfasser (DE-588)172015464 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007892899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bardi, Martino 1956- Capuzzo Dolcetta, Italo 1948- Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations Commande, Théorie de la Commande, Théorie de la ram Jeux différentiels Jeux différentiels ram Solutions de viscosité Control theory Differential games Viscosity solutions Viskositätslösung (DE-588)4463279-4 gnd Differentialspiel (DE-588)4012253-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd |
| subject_GND | (DE-588)4463279-4 (DE-588)4012253-0 (DE-588)4121428-6 (DE-588)4158954-3 |
| title | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations |
| title_auth | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations |
| title_exact_search | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations |
| title_full | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations Martino Bardi ; Italo Capuzzo-Dolcetta |
| title_fullStr | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations Martino Bardi ; Italo Capuzzo-Dolcetta |
| title_full_unstemmed | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations Martino Bardi ; Italo Capuzzo-Dolcetta |
| title_short | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations |
| title_sort | optimal control and viscosity solutions of hamilton jacobi bellman equations |
| topic | Commande, Théorie de la Commande, Théorie de la ram Jeux différentiels Jeux différentiels ram Solutions de viscosité Control theory Differential games Viscosity solutions Viskositätslösung (DE-588)4463279-4 gnd Differentialspiel (DE-588)4012253-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd |
| topic_facet | Commande, Théorie de la Jeux différentiels Solutions de viscosité Control theory Differential games Viscosity solutions Viskositätslösung Differentialspiel Optimale Kontrolle Hamilton-Jacobi-Differentialgleichung Dynamische Programmierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007892899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bardimartino optimalcontrolandviscositysolutionsofhamiltonjacobibellmanequations AT capuzzodolcettaitalo optimalcontrolandviscositysolutionsofhamiltonjacobibellmanequations |