A gaussian function network for uncertainty propagation through nonlinear dynamical system

A Gaussian mixture model approach is proposed for accurate uncertainty propagation through a general nonlinear system. The transition probability density function, is approximated by a finite sum of Gaussian density functions whose parameters (mean and covariance) are propagated using linear propagation theory. Further, Fokker-Planck equation error is used as a feedback to adapt for the amplitude of different Gaussian components while solving a convex quadratic programming problem. The proposed method is applied to a variety of test problems in the open literature, and argued to be an excellent candidate for higher dimensional uncertainty propagation problems.