SUFFICIENCY CONDITIONS FOR EXISTENCE OF AN OPTIMAL FEEDBACK-CONTROL IN STOCHASTIC MECHANICS

In the framework of stochastic mechanics. the following problem is considered : in a set of admissible feedback controls v, with range in E(n), find one minimizing the expectation E(SX){integrel-T/S L(t,xi(t),v(t,xi(t)))dt + W(T)(xi(T))} for all (s,x) is-an-element-of [0,T)xE(n), where L(t,x,nu) = (1/2)mnu 2U(t,x) is the classical action integrand and xi is a n-dimensional diffusion process (in the weak sense [17]) with drift v and diffusion coefficient D = constant > 0. W(T) and U are given real functions . Sufficiency conditions for existence of such an optimal feedback control are given.