On differential inclusions with prescribed attainable sets

Abstract

In this article, the inverse problem of the differential inclusion theory is studied. For a given epsilon > 0 and a continuous set valued map t --> W(t), t is an element of [t(0), theta], where W(t) subset of R-n is compact and convex for every t E [t(0), theta], it is required to define differential inclusion so that the Hausdorff distance between the attainable set of the differential inclusion at the time moment t with initial set (to, W(to)) and W(t) would be less than c for every t is an element of [to, theta]