Minimum entropy control for non-linear and non-Gaussian two-input and two-output dynamic stochastic systems

In this study, the problem of control algorithm design for a class of nonlinear two-input and two-output systems with non-Gaussian disturbances is investigated, where a general non-linear auto-regressive moving average with exogenous model is used to describe the system. Based on the deduced probability density functions of tracking errors, a new performance index is established using the entropy and joint entropy so as to characterise the uncertainty of the tracking errors of the closed-loop system. This performance also includes the expectations of tracking errors and the constrains of control energy. A recursive optimisation control algorithm is obtained by minimising the performance index. Moreover, the local stability condition of the closed-loop systems is established after some formulations. Finally, the comparative simulation results are presented to show that the performance of the proposed algorithm is superior to that of proportional-integral-derivative controller.