Moment Characteristic Method in the Optimal Control Theory of Diffusion-Type Stochastic Systems

Abstract

In this paper, we provide a substantive description of one of the methods for solving problems of the optimal programmed control of diffusion-type stochastic systems with a quadratic quality functional on a finite time interval that allows reducing the stochastic formulation of the question to a deterministic one. We try to present the main ideas, advantages, and disadvantages of the method, as well as to outline as widely as possible the range of problems, to which this method can be applied in an accessible (but mathematically rigorous) form. Here, we do not provide technical details of using the method for solving specific problems. However, there are references in the paper, where these details can be found. New results, which are illustrated by examples that are directly related to the well-known applied problems of optimal control, are obtained. A rather comprehensive review of the current practical applications of the moment characteristic method is provided.