Neural optimal control of nonlinear stochastic systems

This paper deals with the problem of designing a feedback control law that drives a dynamic system so as to minimize a given cost function. Random noises act on both the dynamic system and the state observation channel, which may also be nonlinear. Thus general non-LQG optimal control problems are very difficult to solve. The proposed solution is based on two main approximating assumptions: 1) the control law is assigned a given structure in which a finite number of parameters have to be determined in order to minimize the cost function; and 2) the control law is given a “limited memory”, which prevents the amount of data to be stored from increasing overtime. The first assumption enables us to approximate the original functional optimization problem by nonlinear programming. The errors resulting from both assumptions are discussed. Simulation results show that the proposed method constitutes a simple and effective tool for solving, to a sufficient degree of accuracy, optimal control problems traditionally regarded as difficult ones