On differential inclusions with prescribed attainable sets

AbstractIn this article, the inverse problem of the differential inclusion theory is studied. For a given ε>0 and a continuous set valued map t→W(t), t∈[t0,θ], where W(t)⊂Rn is compact and convex for every t∈[t0,θ], 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 (t0,W(t0)) and W(t) would be less than ε for every t∈[t0,θ]