Bardi / Capuzzo-Dolcetta Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations

1. Auflage, 1997, 2. printing 2009
ISBN: 978-0-8176-4755-1
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 574 Seiten, eBook

Reihe: Modern Birkhäuser Classics

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.

Zielgruppe

Research

Autoren/Hrsg.

Bardi, Martino

Capuzzo-Dolcetta, Italo

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.