Modeling and Analysis of Output Processes of Linear Continuous Stochastic Systems Based on Orthogonal Expansions of Random Functions

摘要

The problem of modeling and analyzing output processes of linear continuous stochastic systems is considered and the method for its solution based on the spectral form of mathematical description of the control systems is proposed. The proposed approach provides an explicit representation of the output signal of the system in the form of functional series with random coefficients or in the form of a partial sum in the approximate solution, which distinguishes this method from other approaches when the result of the solution are the deterministic characteristics of the output signal: the first two moments or the probability density function. As an application, the problem of modeling the action of wind is considered using the Dryden shaping filter.