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

Martino Bardi, Italo Capuzzo-Dolcetta (Autoren)

Buch | Softcover

574 Seiten

2008 | 1st ed. 1997. 2nd printing 2008. Softcover reprint of the original 1st ed. 1997
Birkhauser Boston Inc (Verlag)
9780817647544 (ISBN)

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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.

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.

Reihe/Serie	Modern Birkhäuser Classics
Zusatzinfo	16 Illustrations, black and white
Verlagsort	Secaucus
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-13	9780817647544 / 9780817647544
Zustand	Neuware