Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACT

In this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.

KEYWORDS:

• Active disturbance rejection control
• extended state observer
• MIMO nonlinear systems
• stochastic disturbance
• stabilisation

AMS subject classifications:

• 93B52
• 37L15
• 93D15
• 93B51

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ze-Hao Wu http://orcid.org/0000-0003-4109-1757

Bao-Zhu Guo http://orcid.org/0000-0001-9078-0001

Additional information

Funding

This work was carried out with the support of the National Natural Science Foundation of China [grant number 11501108], the Natural Science Foundation of Guangdong Province [grant number 2015A030313636], and the Project of Department of Education of Guangdong Province [grant numbers 2017KTSCX191, 2017KZDXM087, 2017KQNCX209].