Approximation of the viability kernel
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.
scientific article; zbMATH DE number 528775