A method of approximating attainability sets for differential inclusions with a specified accuracy (Q1176919)

A method for approximating the attainability set \(X(t)\) of a differential inclusion \(\dot x\in F(t,x)\), \(x(0)\in X_ 0\), \(0\leq t\leq T\), is presented. The method provides a prescribed accuracy which means that for a prescribed \(\delta\) a mapping \(Y: [0,T]\to \{M: M\subset \mathbb{R}^ n, M\hbox{-compact}\}\) is constructed in such a way that \(h(X(t),Y(t))\leq \delta\) for \(0\leq t\leq T\), where \(h(\cdot,\cdot)\) is the Hausdorff distance between sets in \(\mathbb{R}^ n\).