Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics
type: Item
instance of: scholarly article
title: Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics
zbMATH Open document ID: 0961.49021
author: A. V. Sarychev
author: Delfim F. M. Torres
published in: Applied Mathematics and Optimization
publication date: 2001-05-06T00:00:00Z
review text: The paper deals with the Lagrange optimal control problem with a cost functional \(\int_a^b L(t,x,\dot{x}) dt\) and control-affine dynamics \(\dot{x}=f(t,x)+g(t,x)u\). The main object of study is the boundedness of optimal controls \(u\), corresponding to the Lipschitz regularity of minimizers for the basic problem of the calculus of variations. The main result of the paper is Theorem 1, where boundedness of controls is achieved reducing first the original problem to an autonomous time-optimal control problem, and then applying the Pontryagin maximum principle. This method has been first used, for the purpose of proving existence, by Gamkrelidze. Applications to the regularity of solutions of the basic problem of the calculus of variations (comparing the results to those of Clarke and Vinter) and to variational problems involving higher order derivatives are given.
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 1406322
zbMATH Keywords: Lipschitz regularity
zbMATH Keywords: Pontryagin maximum principle
zbMATH Keywords: optimal control
Wikidata QID: Q60224850
reviewed by: Luigi Ambrosio
MaRDI profile type: Publication
full work available at URL: s002459911013
OpenAlex ID: W2040808690
DOI: 10.1007/S002459911013
description: scientific article; zbMATH DE number 1406322