Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations

- Preface
- Basic notations
- 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
- Numerical solution of Dynamic Programming
- Nonlinear H-infinity control by Pierpaolo Soravia
- Bibliography
- Index

"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. The book may be used by graduate students and researchers in control theory both as an introductory textbook, and as an up-to-date reference book." -Mathematical Reviews"The work is self-contained and is written in an accessible style with discussions of difficult questions on simplified model problems, with useful sections of bibliographical and historical notes and rich sets of proposed exercises at the end of each section. It may be easily used for graduate courses on various topics in control theory. We recommend it to both students and researchers interested in this area of applied mathematics." -Revue Roumaine de Mathématiques Pures et Appliquées"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 oppinion, 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