On the Method of Successive Approximations for Dynamic Optimization of a Nonlinear Control System Subjected to a Stationary Gaussian Random Disturbance

Abstract

In this paper, an analytical method of finding the suboptimal controller for a plant consisting of n-th order servosystem with the control signal θ (t) constrained by the condition that |θ (t)|=1 and a stationary Gaussian white noise is presented. The performance criterion considered here is the mathematical expectation of the integrated value of the mean-squared error. By using the dynamic programming method, the problem of this synthesis is reducible to the problem of solving a parabolic partial differential equation for the criterion function. Since, as a rule, it is very difficult actually to carry out the calculations, we use an approximate asymptotic method for the solution of such equations. That is, we asume that solution is expanded to the power series with respect to the dispersion of disturbance, at each approximation, it is determined in such manner as satisfies the necesary condition for optimality.