Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1997
|
| Schriftenreihe: | Systems & Control: Foundations & Applications
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems…will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." — Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises…Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." — ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." — Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." — Acta Applicandae Mathematicae |
| Beschreibung: | 1 Online-Ressource (XVII, 574 p) |
| ISBN: | 9780817647551 9780817647544 |
| DOI: | 10.1007/978-0-8176-4755-1 |
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Datensatz im Suchindex
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| building | Verbundindex |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
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| id | DE-604.BV042419155 |
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817647551 9780817647544 |
| language | English |
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| physical | 1 Online-Ressource (XVII, 574 p) |
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| spelling | Bardi, Martino Verfasser aut Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations by Martino Bardi, Italo Capuzzo-Dolcetta Boston, MA Birkhäuser Boston 1997 1 Online-Ressource (XVII, 574 p) txt rdacontent c rdamedia cr rdacarrier Systems & Control: Foundations & Applications This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems…will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." — Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises…Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." — ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." — Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." — Acta Applicandae Mathematicae Mathematics Differential equations, partial Systems theory Mathematical optimization Systems Theory, Control Optimization Partial Differential Equations Mathematik Viskositätslösung (DE-588)4463279-4 gnd rswk-swf Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 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 s Viskositätslösung (DE-588)4463279-4 s Optimale Kontrolle (DE-588)4121428-6 s Differentialspiel (DE-588)4012253-0 s 1\p DE-604 Capuzzo-Dolcetta, Italo Sonstige oth https://doi.org/10.1007/978-0-8176-4755-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bardi, Martino Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations Mathematics Differential equations, partial Systems theory Mathematical optimization Systems Theory, Control Optimization Partial Differential Equations Mathematik Viskositätslösung (DE-588)4463279-4 gnd Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd Differentialspiel (DE-588)4012253-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4463279-4 (DE-588)4158954-3 (DE-588)4012253-0 (DE-588)4121428-6 |
| 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 by Martino Bardi, Italo Capuzzo-Dolcetta |
| title_fullStr | Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations by Martino Bardi, Italo Capuzzo-Dolcetta |
| title_full_unstemmed | Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations by 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 | Mathematics Differential equations, partial Systems theory Mathematical optimization Systems Theory, Control Optimization Partial Differential Equations Mathematik Viskositätslösung (DE-588)4463279-4 gnd Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd Differentialspiel (DE-588)4012253-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Mathematics Differential equations, partial Systems theory Mathematical optimization Systems Theory, Control Optimization Partial Differential Equations Mathematik Viskositätslösung Hamilton-Jacobi-Differentialgleichung Differentialspiel Optimale Kontrolle |
| url | https://doi.org/10.1007/978-0-8176-4755-1 |
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