A rational spline model approximation and control of output probability density functions for dynamic stochastic systems

This paper presents a new method to model and control the shape of the output probability density functions for dynamic stochastic systems subjected to arbitrary bounded random input. A new rational model is proposed to approximate the output probability density function of the system. This is then followed by the design of a novel nonlinear controller, which guarantees the monotonic decreasing of the functional norm of the difference between the measured probability density function and its target distribution. This leads to a desired tracking performance for the output probability density function. A simple example is utilized to demonstrate the use of the proposed modelling and control algorithm and encouraging results have been obtained.