Two main approximations are used to solve a nonlinear-quadratic-Gaussian (LQG) optimal control problem : the control law is assigned a given structure in which a finite number of parameters have to be determined to minimize the cost function (the chosen structure is that of a multilayer feedforward neural network), and the control law is given a "limited memory." The errors resulting from both assumptions are discussed. Simulation results show that the proposed method may constitute a simple and effective tool for solving, to a sufficient degree of accuracy, optimal control problems traditionally regarded as difficult ones.