Approximate extreme solutions for evolutional inclusions of subdifferential type

Abstract

The problem of finding of approximate optimal feedback control was considered for an evolutional inclusion of the subdifferential type, perturbed by εF(y), where ε>0 is a small parameter and F is a multivalued mapping. On condition that for ε=0 the problem has unique solution u[t,y] in the feedback form, it was proved that the formula u[t,y] provides an approximate synthesis for the initial problem for small ε>0.