On differential inclusions with prescribed attainable sets ✩

In 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].  2003 Elsevier Science (USA). All rights reserved.