Approximation of the viability kernel
type: Item
instance of: scholarly article
title: Approximation of the viability kernel
zbMATH Open document ID: 0790.65081
DOI: 10.1007/BF01204182
author: Patrick Saint-Pierre
published in: Applied Mathematics and Optimization
publication date: 1994-06-16T00:00:00Z
review text: Let \(X\) be a finite-dimensional vector space, \(K\) a compact subset of \(X\). In the paper the viability kernel \(V\) (\(V_ \rho\)) of \(K\) under \(F\) (\(G_ \rho\)) of the differential inclusion \(\dot x(t) \in F(x(t))\), \(x(0) = x_ 0 \in K\) (of its discrete explicit scheme \(x^{n+1} \in G_ \rho(x^ n)\), \(n \geq 0\), \(G_ \rho = 1 + \rho F\), i.e. \((x^{n+1} - x^ n)/\rho \in F(x^ n))\) is studied where \(F\) is a Marchaud map from \(K\) to \(X\). It is proved that, for a good choice of discretizations, the sequence of \(V_ \rho\) converges to \(V\) if \(F\) is Lipschitzian.
Mathematics Subject Classification ID: 65L99
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 528775
zbMATH Keywords: convergence
zbMATH Keywords: viability kernel
zbMATH Keywords: differential inclusion
zbMATH Keywords: Marchaud map
zbMATH Keywords: choice of discretizations
reviewed by: Miroslav Bartušek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 528775