Anti-disturbance control based on nonlinear disturbance observer for a class of stochastic systems

Abstract

In engineering, there exist lots of nonlinear disturbance dynamics, which can be described by nonlinear exogenous systems. The current stochastic linear disturbance observer is conservative and is not applicable for nonlinear disturbance dynamics. This paper studies a class of stochastic systems with multiple disturbances, including white noise and disturbances modelled by a nonlinear exogenous system. To estimate the disturbance with nonlinear dynamics, a stochastic nonlinear disturbance observer is proposed. Based on the observer, a nonlinear disturbance observer-based disturbance attenuation control (NDOBDAC) scheme is constructed such that the composite closed-loop system is asymptotically mean-square bounded. According to the simulation example, the state responses of the system diverge in the absence of control, but it tends to be $\pm 0.01$ under NDOBDAC, which demonstrates the effectiveness of the proposed scheme. In addition, the anti-disturbance control accuracy of NDOBDAC approximately improves $60~200$ times compared with $H_{\infty }$ control and active disturbance rejection control (ADRC). The simulation results demonstrate the feasibility and effectiveness of the proposed scheme.