Control of systems to sets and their interiors
type: Item
instance of: scholarly article
title: Control of systems to sets and their interiors
zbMATH Open document ID: 0843.93009
DOI: 10.1007/BF02192020
author: P. R. Wolenski
author: F. H. Clarke
published in: Journal of Optimization Theory and Applications
publication date: 1996-03-04T00:00:00Z
review text: For a differential inclusion \(\dot x\in F(t, x)\) and for a target set \(S\subset \mathbb{R}^n\) the problems of local weak (by some trajectory \(x(t)\) of the inclusion) and strong (by all trajectories \(x(t)\)) attainability of \(S\) are considered. The authors give the sufficient conditions for such attainability in terms of proximal normals and proximal subgradients. The proofs are based upon the time discretization method. The authors show that for the problem under consideration, the known state continuity assumption on the right-hand side \(F(t, x)\) of the differential inclusion can be weakened to upper semicontinuity in \(x\). The problems of weak and strong penetration at a point \(x\) are also studied (the penetration property means that for a fixed point \(x\) on the boundary of \(S\) some trajectory \(x(t)\) (for weak penetration) or every trajectory \(x(t)\) (for strong penetration) with a condition \(x(0)= x\) lies in the interior of \(S\) for small \(t>0\)). For these problems the target set \(S\) is assumed to be epicontinuous near \(x\). Three examples are given to illustrate the role of the hypotheses.
reviewed by: T. F. Filippova
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 851108
zbMATH Keywords: differential inclusion
zbMATH Keywords: attainability
zbMATH Keywords: proximal normals
zbMATH Keywords: proximal subgradients
zbMATH Keywords: time discretization
zbMATH Keywords: penetration property
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02192020
OpenAlex ID: W2095072256
description: scientific article; zbMATH DE number 851108