Optimal control of non-linear stochastic systems by approximation of the optimal cost functional

Among the deterministic policies for the optimal control of stochastic systems the best one is of closed-loop type, because it presents the "dual effect" of control. The theoretical closed-loop solution structure is deduced from Bellman's principle but is very difficult to implement in the non-linear case. This communication presents a closed-loop solution by approximation of the minimum cost function by introduction of the gaussian sum method.