Nonlinear stochastic control via stationary probability density functions

This paper presents a control strategy for externally excited stochastic systems with parametric uncertainties. The objective is to drive the system to match a target probability density function (PDF) in steady state. The control consists of a nonlinear feedback and a switching term for handling parameter uncertainty. The fast rate of convergence to the stationary PDF is observed in the time evolution of the mean and variance of the closed loop system through Monte Carlo simulations. The dependence of the control performance on the number of terms in the polynomial control series and on the rate of convergence to the steady state distribution are studied numerically. This control design based on the stationary PDF is also applied to the tracking of a time-varying probability density function.