Cannarsa / Sinestrari Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

Erscheinungsjahr 2007
ISBN: 978-0-8176-4413-0
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 58, 304 Seiten, eBook

Reihe: Progress in Nonlinear Differential Equations and Their Applications

Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations.The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions.

Zielgruppe

Research

Autoren/Hrsg.

Cannarsa, Piermarco

Sinestrari, Carlo

Inhaltsverzeichnis

A Model Problem.- Semiconcave Functions.- Generalized Gradients and Semiconcavity.- Singularities of Semiconcave Functions.- Hamilton-Jacobi Equations.- Calculus of Variations.- Optimal Control Problems.- Control Problems with Exit Time.