Sharif Digital Repository

To analyze a highly nonlinear dynamical system, it is necessary to evaluate the time evolution of the probability density function (pdf) of the states. In this paper, a novel Gaussian sum method is proposed to approximate the non-Gaussian pdf of a dynamical system whose nonlinear elements depend only on a single state variable. Using the Chapman-Kolmogorov equation, a set of recursive equations is derived to propagate the mean, covariance, and weight of the Gaussian sum components. There are several multiple integrals in the recursive equations which are analytically reduced to single integrals. As an application, the proposed approach is applied to statistically analyze the engagement of...