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 inEⁿ, find one minimizing the expectationE_sx{_s^TL(t, (t), (t, (t)))dt + W_T((T))} for all (s, x) [0,T) Eⁿ, whereL(t, x, ) = (/12)m²– U(t, x) is the classical action integrand and is an-dimensional diffusion process in the weak sense, (see Bensoussan, 1982) with drift and diffusion coefficientD constant > 0.W_T andU are given real functions. Sufficiency conditions for the existence of such an optimal feedback control are given.Dedicated to George LeitmannRecommended by G.J. OlsderPresented at the Third Workshop on Control Mechanics in honor of George Leitmann, January 22–24, 1990, University of Southern California, Los Angeles, California (USA).