The construction of approximate integral funnels of differential inclusions (Q1903919)

An algorithm of polyhedral approximation of integral funnel of a differential inclusion is proposed. It is assumed that the multifunction in the right-hand side is convex-valued and Lipschitz continuous. Moreover, it is supposed that it can be uniformly approximated by the convex hull of a finite family of Lipschitz continuous single-valued functions. Under additional assumptions of regularity, a first-order estimate of approximation is obtained. As an illustration, the proposed approximation scheme is applied in a population dynamics model.