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

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

by Martino Bardi, Italo Capuzzo-Dolcetta
     
 

ISBN-10: 0817636404

ISBN-13: 9780817636401

Pub. Date: 12/28/1997

Publisher: Birkhauser Verlag

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.

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Overview

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

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Product Details

ISBN-13:
9780817636401
Publisher:
Birkhauser Verlag
Publication date:
12/28/1997
Series:
Systems and Control Series
Pages:
596
Product dimensions:
6.14(w) x 9.21(h) x 1.38(d)

Table of Contents

Preface
Basic notations
Ch. IOutline of the main ideas on a model problem1
Ch. IIContinuous viscosity solutions of Hamilton-Jacobi equations25
Ch. IIIOptimal control problems with continuous value functions: unrestricted state space97
Ch. IVOptimal control problems with continuous value functions: restricted state space227
Ch. VDiscontinuous viscosity solutions and applications285
Ch. VIApproximation and perturbation problems359
Ch. VIIAsymptotic problems397
Ch. VIIIDifferential Games431
App. ANumerical Solution of Dynamic Programming Equations471
App. BNonlinear [actual symbol not reproducible] control505
Bibliography533
Index565

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