On convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems

ABSTRACT

In this paper, the practical mean-square convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems modelled by the Itô-type stochastic differential equations with vast stochastic uncertainties is developed. We first design an extended state observer (ESO) to estimate both the unmeasured states and the stochastic total disturbance which includes unknown internal system dynamics, external stochastic disturbance without known statistical characteristics, unknown stochastic inverse dynamics, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then cancelled (compensated) in the feedback loop. An ESO-based output-feedback control is finally designed analogously as for the system without uncertainties. The practical mean-square reference tracking and practical mean-square stability of the resulting closed-loop system are achieved. The numerical experiments are carried out to illustrate the effectiveness of the proposed approach.

KEYWORDS:

• Stochastic nonlinear systems
• active disturbance rejection control
• extended state observer
• stochastic disturbance
• reference tracking
• stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was carried out with the support of the Key University Project of Guangdong Province [grant number 2014KZDXM063]; and Natural Science Foundation of Guangdong Province [grant number 2015A030313636].