Optimal Control and Viscosity Solutions of...

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Beschreibung

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.

Zusammenfassung

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. This is an affordable new softcover edition of a bestselling text replete with exercises. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. 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.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2008
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Modern Birkhäuser Classics
Inhalt:	xvii 574 S. 16 s/w Illustr. 574 p. 16 illus.
ISBN-13:	9780817647544
ISBN-10:	0817647546
Sprache:	Englisch
Herstellernummer:	12171750
Einband:	Kartoniert / Broschiert
Autor:	Bardi, Martino Capuzzo-Dolcetta, Italo
Hersteller:	Birkhäuser Birkhäuser Boston Modern Birkhäuser Classics
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 32 mm
Von/Mit:	Martino Bardi (u. a.)
Erscheinungsdatum:	11.01.2008
Gewicht:	0,89 kg