Evaluation of the Non-Stationary Probability Densities in a Bang-Bang Control System

Abstract

This paper presents a numerical method of evaluating the density of probability distribution of a Bang-Bang control system excited by various types of pre-assigned signals in the presence of a Gaussian random noise. Namely, the Fokker-Plant-Kolomogorov equation for the probability density function may be solved as approximate solution of the given third boundary-value problem. For this purpose, the boundary conditions are applied along the switching surface in such a manner that the energy integral for the probability density function has a minimum value. Finally, the moments for the probability density function are calculated, and the convergency for the method of finite differences is examined.