An optimal control problem with various quality functionals (Q917013)

A numerical method for recovering a convex set F from its support function c(F,\(\psi\)) is considered: a polyhedron \(\bar F\) is constructed such that the Hausdorff distance between F and \(\bar F\) does not exceed a given accuracy \(\epsilon >0\) and \(F\subset \bar F\). The obtained result is applied to the recovery of the attainable set of a linear control system from its support function. From the knowledge of the recovered attainable set it is possible to solve the optimal control problem with various terminal functionals.