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Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

✍ Scribed by Cannarsa P., Sinestrari C.

Year
2004
Tongue
English
Leaves
193
Edition
book draft
Category
Library
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✦ Synopsis

This text details the theory of semiconcave functions and describes the role they play in optimal control and Hamilton-Jacobi equations. Part I covers the general theory, summarizing and illustrating key results with significant examples. Part II is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. Singularities are also studied for general semiconcave functions, then sharply estimated for solutions of Hamilton-Jacobi equations, and finally analyzed in connection with optimal trajectories of control systems. State-of-the-art reference for researchers in optimal control, the calculus of variations, and PDEs, as well as a good introduction for graduate students to modern dynamic programming for nonlinear control systems.

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