Multivalued dynamics on a closed domain with absorbing boundary. Applications to optimal control problems with integral constraints
type: Item
instance of: scholarly article
title: Multivalued dynamics on a closed domain with absorbing boundary. Applications to optimal control problems with integral constraints
zbMATH Open document ID: 0961.34003
DOI: 10.1016/S0362-546X(98)00301-0
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-05-16T00:00:00Z
review text: The authors consider the following differential inclusion: \[ \dot{y} \in F(s,y), \tag{1} \] where \(F:\mathbb{R}\times \mathbb{R}^n \to \mathbb{R}^n\) is a multifunction, and they study the problem of finding suitable conditions in order to obtain the lower semicontinuity of the solution map, which is the multifunction that to each \((t,x) \in \mathbb{R} \times \mathbb{R}^n\) associates all trajectories (solutions to equation (1)) issuing from \(x\) at time \(t\). This property has applications in the theory of optimal control problems as the same authors show in the final part of their paper. The authors introduce a condition and they prove that it is sufficient to assure the lower semicontinuity of the solution map. This condition is an extension of some introduced before and it is proved that it can be applied, for example, to the case of a control system with an integral constraint.
reviewed by: Francesca Papalini
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 1512499
zbMATH Keywords: Lipschitz differential inclusions
zbMATH Keywords: state constraints
zbMATH Keywords: minimum problems
author: M. Motta
author: Franco Rampazzo
MaRDI profile type: Publication
Wikidata QID: Q127342858
description: scientific article; zbMATH DE number 1512499