Extended state observer for MIMO nonlinear systems with stochastic uncertainties

ABSTRACT

In this paper, both linear extended state observer (ESO) and nonlinear ESO with homogeneous weighted functions are proposed for a class of multi-input multi-output (MIMO) nonlinear systems composed of coupled subsystems with large stochastic uncertainties. The stochastic uncertainties in each subsystem including internal coupled unmodelled dynamics and external stochastic disturbance without known statistical characteristics are lumped together as the stochastic total disturbance (extended state) of each subsystem. The linear ESO and nonlinear ESO are designed separately for real-time estimation of not only the unmeasured state but also the stochastic total disturbance of each subsystem. The practical mean square convergence of these two classes of ESOs are developed. Some numerical simulations are presented to demonstrate the effectiveness of the ESOs with the advantages of smaller peaking values and more accurate estimation by the nonlinear ESO.

Keywords:

• Extended state observer
• active disturbance rejection control
• MIMO nonlinear systems
• stochastic uncertainties
• unmodelled dynamics

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 numbers 11501108, 11501106], the Project of Department of Education of Guangdong Province [grant numbers 2017KTSCX191, 2017KZDXM087, 2014KZDXM063], and the Natural Science Foundation of Guangdong Province [grant numbers 2015A030313636, 2016A030313835].