On the construction of differential inclusion with prescribed integral funnel

Abstract

In this article, the inverse problem of the differential inclusion theory is considered. For a given $varepsilon$>0 and a given special type set valued map t$rightarrow$V(t), t $in$ [$t_ast$,$t^ast$], it is required to define differential inclusion such that the Hausdorff distance between the reachable sets of the differential inclusion with initial set ($t_ast$,V($t_ast$)) and V(t) would be less than $varepsilon$ for every t $in$ [$t_ast$,$t^ast$].