Neural approximations for multistage optimal control of nonlinear stochastic systems

This paper deals with the problem of designing a feedback control law that drives a dynamic system (in general, nonlinear) so as to minimize a given cost function (in general, nonquadratic). Random noises (in general, non-Gaussian) act on both the dynamic system and the state observation channel, which may be nonlinear, too. As is well known, so 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 (the chosen structure is that of a multilayer feedforward neural network), and (2) the control law is given a "limited memory", which prevents the amount of data to be stored from increasing over time. The first assumption; enables the authors to approximate the original functional optimization problem by a nonlinear programming one. 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.