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Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control Piermarco Cannarsa

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control By Piermarco Cannarsa

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control by Piermarco Cannarsa

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Summary

Presents an exposition of the theory of semi-concave functions and their role in optimal control and Hamilton-Jacobi equations. Divided into two parts, this book covers the general theory in the first part. It covers applications concerning the Bolza problem in the calculus of variations and optimal exit time problems in the second part.

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control Summary

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control by Piermarco Cannarsa

* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems, by leading experts in the field

* A central role in the present work is reserved for the study of singularities

* Graduate students and researchers in optimal control, the calculus of variations, and PDEs will find this book useful as a reference work on modern dynamic programming for nonlinear control systems

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control Reviews

The main purpose of this book is to provide a systematic study of the notion of semiconcave functions, as well as a presentation of mathematical fields in which this notion plays a fundamental role. Many results are extracted from articles by the authors and their collaborators, with simplified-and often new-presentation and proofs.... One of the most attractive features of this book is the interplay between several fields of mathematical analysis.... Despite the many topics addressed in the book, the required mathematical background for reading it is limited because all the necessary notions are not only recalled, but also carefully explained, and the main results proved.

The book will be found very useful by experts in nonsmooth analysis, nonlinear control theory and PDEs, in particular, as well as by advanced graduate students in this field. They will appreciate the many detailed examples, the clear proofs and the elegant style of presentation, the fairly comprehensive and up-to-date bibliography and the very pertinent historical and bibliographical comments at the end of each chapter.

-Mathematical Reviews

Table of Contents

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.

Additional information

NPB9780817640842
9780817640842
0817640843
Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control by Piermarco Cannarsa
Piermarco Cannarsa
Progress in Nonlinear Differential Equations and Their Applications
New
Hardback
Birkhauser Boston Inc
2004-03-22
304
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control