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＜電子ブック＞
Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control / by Piermarco Cannarsa, Carlo Sinestrari
(Progress in Nonlinear Differential Equations and Their Applications. ISSN:23740280 ; 58)

版	1st ed. 2004.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2004
本文言語	英語
大きさ	XIV, 304 p : online resource
著者標目	*Cannarsa, Piermarco author Sinestrari, Carlo author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Measure theory LCSH:Mathematical optimization FREE:Differential Equations FREE:Measure and Integration FREE:Optimization
一般注記	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 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. A central role in the present work is reserved for the study of singularities. Singularities are first investigated for general semiconcave functions, then sharply estimated for solutions of Hamilton–Jacobi equations, and finally analyzed in connection with optimal trajectories of control systems. Researchers in optimal control, the calculus of variations, and partial differential equations will find this book useful as a state-of-the-art reference for semiconcave functions. Graduate students will profit from this text as it provides a handy—yet rigorous—introduction to modern dynamic programming for nonlinear control systems HTTP:URL=https://doi.org/10.1007/b138356

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