Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
This softcover 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.
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Boston, MA
Birkhäuser
1997
Birkhäuser Boston Birkhauser |
| Edition | 1 |
| Series | Modern Birkhäuser Classics |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9780817647544 0817647546 9781489902603 1489902600 9780817636401 0817636404 |
| DOI | 10.1007/978-0-8176-4755-1 |
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| Abstract | This softcover 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. |
|---|---|
| AbstractList | The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of Hamilton-Jacobi type and its applications to optimal deterministic control and differential games. The theory of viscosity solutions, initiated in the early 80's by the papers of M.G. Crandall and P.L. Lions [CL81, CL83], M.G. Crandall, L.C. Evans and P.L. Lions [CEL84] and P.L. Lions' influential monograph [L82], provides an - tremely convenient PDE framework for dealing with the lack of smoothness of the value functions arising in dynamic optimization problems. The leading theme of this book is a description of the implementation of the viscosity solutions approach to a number of significant model problems in op- real deterministic control and differential games. We have tried to emphasize the advantages offered by this approach in establishing the well-posedness of the c- responding Hamilton-Jacobi equations and to point out its role (when combined with various techniques from optimal control theory and nonsmooth analysis) in the important issue of feedback synthesis. 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. This softcover 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. |
| Author | Capuzzo-Dolcetta, Italo Bardi, Martino |
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| Copyright | Birkhäuser Boston 1997 |
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| DOI | 10.1007/978-0-8176-4755-1 |
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| Edition | 1 1st Edition 1997th 2nd printing 2008 Softcover rep |
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| Notes | Includes bibliographical references (p. [533]-564) and index Reprint of the 1997 edition "Originally published in the series Systems & Control: Foundations & Applications"--T.p. verso |
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| PublicationSeriesTitle | Modern Birkhäuser Classics |
| PublicationYear | 1997 |
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| Snippet | This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton-Jacobi type and... 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... The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of... |
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| SubjectTerms | Control theory Differential equations, partial Differential games Mathematical optimization Mathematics Mathematics and Statistics Optimization Partial Differential Equations Systems theory Systems Theory, Control Viscosity solutions |
| TableOfContents | Intro -- Modern Birkhäuser Classics -- Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations -- Copyright -- Contents -- Preface -- Basic notations -- CHAPTER I Outline of the main ideas on a model problem -- CHAPTER II Continuous viscosity solutions of Hamilton-Jacobi equations -- CHAPTER III Optimal control problems with continuous value functions: unrestricted state space -- CHAPTER IV Optimal control problems with continuous value functions: restricted state space -- CHAPTER V Discontinuous viscosity solutions and applications -- CHAPTER VI Approximation and perturbation problems -- CHAPTER VII Asymptotic problems -- CHAPTER VIII Differential Games -- APPENDIX A Numerical Solution of Dynamic Programming Equations -- APPENDIX B Nonlinear H∞ control -- Bibliography -- Index Outline of the main ideas on a model problem -- Continuous viscosity solutions of Hamilton-Jacobi equations -- Optimal control problems with continuous value functions: unrestricted state space -- Optimal control problems with continuous value functions: restricted state space -- Discontinuous viscosity solutions and applications -- Approximation and perturbation problems -- Asymptotic problems -- Differential Games. |
| Title | Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations |
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