On differential inclusions with prescribed attainable sets (Q1868801)

The paper concerns an inverse problem for differential inclusions. It is shown that, to a given set-valued map \(t\in[t_0,\theta]\to{W(t)}\subseteq\mathbb{R}^n\), for every \(\varepsilon\geq 0\) there is a set-valued map \((t,x)\in[t_0,\theta]\times\mathbb{R}^n\to P(t,x)\subseteq \mathbb{R}^n\) such that the attainable sets \(Y(t)\) generated by the differential system \(\dot{x}(t)\in P(t,x(t))\), \(x(t_0)\in W(t_0)\), satisfy the inequality \(h(Y(t),W(t))\leq\varepsilon\). Here, \(h(E,D)\) stands for the Hausdorff distance between the sets \(D\) and \(E\). Since \(W\) is compact, convex-valued and continuous, so is \(P\).