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 DHX(t) = F(t, X(t), H(t, X(t))), X(0) = X0, for all t ∈ [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.