Joint PDF Tracking Control for a Class of Multivariate Time-Varying Stochastic Descriptor Systems

This paper considers a new tracking control problem for a class of nonlinear stochastic descriptor systems, where the tracked target is a given joint probability density function (JPDF). The controlled plants can be represented by multivariate discrete-time descriptor systems with non-Gaussian disturbances and nonlinear output equations. The control objective is to find crisp algorithms such that the conditional output JPDFs can follow the given target JPDF. Rather than using statistic methods such as Bayesian estimation or Monte Carlo methods, we establish a direct relationship between the JPDFs of the transformed tracking error and the stochastic input. An optimization approach is applied to present recursive algorithms such that the distances between the output distributions and the desired one are minimized. Furthermore, a stabilization suboptimal control strategy is proposed by using of LMI-based Lyapunov theory. Simulations are provided to demonstrate the effectiveness of the stochastic tracking control algorithms.