Non-Gaussian disturbance rejection control for multivariate stochastic systems using moment-generating function

Abstract

In this paper, a non-Gaussian disturbance rejection control algorithm for a class of nonlinear multivariate stochastic systems is studied. Based on the moment-generating functions obtained from the deduced probability density functions of the output tracking errors, a new criterion representing the stochastic properties of the system is proposed, motivated by a minimum entropy design. A time-variant linear model can be established by the sampled moment-generating functions. Using this model, a control algorithm is developed that minimizes the newly developed criterion. Moreover, a stability analysis is performed for the closed-loop control system. Finally, simulation results of a numerical example demonstrate the effectiveness of the presented control algorithm. The contribution and novelty of this work can be summarized as follows: (1) a novel non-Gaussian disturbance rejection control scheme is proposed based on the minimum entropy principle, (2) the randomness of the multi-variable non-Gaussian stochastic nonlinear system is attenuated based on the new performance criterion, (3) a theoretical convergence analysis has been given for the proposed control system, and (4) a potential framework has been established for the design of a general stochastic system control.