Time-Lag Control Systems

absolutely continuous admissible pair Akad analytic Appl assume Automat Bellman bounded boundedness C(Iſo compact set components Consider continuous function control systems converges convex set corresponding defined Definition denote difference-differential equations differential equations differential-difference equations Dokl Dynamic Programming équation equation x(t equations with retarded exists finite formula functional V(t Hence I(to inequality initial condition x(t initial function h(t interval Iſto Iſa Iſo Iſt kernel matrices lagging argument Lebesgue integrable Lemma Let x(t Lipschitz constant Lipschitzian with respect Math matrix measurable function Mech n-dimensional Nauk SSSR nonlinear optimal control optimal pair optimal problem parameter Proc Proof retarded argument right-hand side ſ KG ſ ſ satisfies the initial second kind Section sequence set C(T ſº solution x(t space stability support hyperplane system X t e Iſto Theorem theory trajectory uniformly Univ vector function