Time-Dependent Probability Distribution of the Non-Stationary Response of Nonlinear Control Systems

Abstract

In this paper, to evaluate the time-dependent probability density function of the response of nonlinear control systems subjected to a suddenly applied Gaussian random input, an approximate method of solving the combined Fokker-Planck equation with the equation of a control system is developed. The basic idea presented here is as follows. The nonlinear transfer characteristic contained in the system is replaced by an equivalent linear one with piecewise linear segments, in the sense of the least square value. The form of probability density function is also replaced by the form of connected Gaussian type probability density function. Under these conceptions, a numerical calculation is carried out. Detailed illustrations are shown by several examples.