Higher Order Statistical Approach to Nonlinear Stochastic Optimal Control Problem

This paper presents the formulation of an optimal control methodology for nonlinear stochastic systems, where the control objective is to obtain a feedback law that would minimizes the higher order statistics associated with the traditional integral quadratic cost. The two part control scheme proposed here consist of approximating the probability density function associated with the nonlinear plant by the Gaussian sum approach and utilizing the existing deterministic optimal control schemes to obtain a feedback law that would minimize the higher order statistics that is of interest. Since both components are interdependent, an iterative scheme is required to obtain the optimal solution.