Measure driven differential inclusions
type: Item
instance of: scholarly article
title: Measure driven differential inclusions
zbMATH Open document ID: 0877.49004
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-12-08T00:00:00Z
review text: The authors discuss the concept of robust solution to the measure driven differential inclusion \[ dx(t)\in F(t,x(t))dt+ G(t,x(t))\mu(dt)\quad\text{on }[0,1],\;x(0)=b. \] Here, \(F\) and \(G\) are given multivalued mappings, the initial value \(b\) is a given point in \(\mathbb{R}^n\), and \(\mu\) is some nonnegative scalar-valued measure on the Borel subsets of \([0,1]\). The case in which \(F\) and \(G\) are single-valued mappings, has been previously considered by \textit{G. Dal Maso} and \textit{F. Rampazzo} [Differ. Integral Equ. 4, No. 4, 739-765 (1991; Zbl 0731.34087)]. One of the issues raised by the present paper concerns the stability properties of robust solutions: under suitable assumptions, it is shown that robust solutions to perturbations of a nominal measure driven differential inclusion yield a solution to the nominal differential inclusion in the limit.
reviewed by: Alberto Seeger
Mathematics Subject Classification ID: 49J24
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 934207
zbMATH Keywords: relaxation
zbMATH Keywords: optimal control
zbMATH Keywords: measure driven differential inclusion
zbMATH Keywords: multivalued mappings
zbMATH Keywords: robust solutions
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0344
OpenAlex ID: W2066616184
DOI: 10.1006/JMAA.1996.0344
description: scientific article; zbMATH DE number 934207