Joint stochastic distribution tracking control for multivariate descriptor systems with non-gaussian variables

Abstract

This article 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. A direct relationship is established between the JPDFs of the transformed tracking error and the stochastic input. An optimisation approach is presented such that the distances between the output JPDF and the desired one are minimised. Furthermore, a stabilisation suboptimal control strategy is proposed using the linear matrix inequality-based Lyapunov theory. Finally, simulations are provided to demonstrate the effectiveness of the stochastic tracking control algorithms.

Keywords:

• probability density function
• stochastic control
• entropy optimisation
• nonlinear control
• descriptor system
• non-Gaussian systems
• tracking control

Acknowledgements

This work is supported by Natural Science Foundation 973 and 863 programme of China.