The PDF shape control of the state variable for a class of stochastic systems

Abstract

The shape control of probability density function (PDF) is an important subject in stochastic systems. The PDF-shaping control study has ranged from linear systems to non-linear systems. In this paper we present a PDF-shaping control technique which is useful for a class of non-linear stochastic systems. Controlling the PDF shape requires designing a controller to make the state PDF follow the goal PDF; it is actually to determine the gains of the controller. As we know, the stationary PDF of the state variable is equivalent to the solution of the Fokker–Planck–Kolmogorov (FPK) equation arising from the stochastic system driven with Gaussian white noise. After designing the controller, we derive the solution with some parameters to the corresponding FPK equation, and then solve out the parameters in the solution by the linear-least-squares method, therefore obtaining the gains of the controller. Finally, simulation experiments have been carried out to verify the effectiveness of the approach.