On maximal and minimal solutions for set-valued differential equations with feedback control

Abstract

In this paper, we present the existence of extremal solutions of set-valued differential equations with feedback control on semilinear Hausdorff space under Hukuhara derivative which is developed under the form D HX(t)=F(t, X(t),H(t,X(t))), X(0)= X 0, for all τ ∈ [0,T] with the monotone iterative technique and we will verify that monotone sequence of approximate solutions converging uniformly to the solution of the problem, that is useful for optimization problems. © 2012 Ngo Van Hoa and Nguyen Dinh Phu.