Control of the output stochastic distributions via Lyapunov function analysis

This paper presents two new methods to control the shape of the output probability density functions for non-Gaussian dynamic stochastic systems, where the rational B-spline model approximation is used. In the first method, the performance function that measures the tracking error between the output probability density function and the desired distribution is used as a Lyapunov function to design the required controller. It has been shown that the output probability density function can asymptotically track the expected distribution and the closed loop system is stable. In the second method, a direct optimal controller is obtained which minimizes the performance function using a nonlinear programming technique.