On Convergence of Extended State Observer for a Class of MIMO Uncertain Stochastic Nonlinear Systems

Extended state observer (ESO) is the key part of active disturbance rejection control, a new control strategy motivated and developed highly from PID's model-free feature. In this paper, both constant gain ESO and time-varying gain ESO are proposed for a class of multi-input multi-output uncertain stochastic nonlinear systems subject to vast stochastic uncertainties. The total stochastic uncertainties in each subsystem including unmodeled dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without known statistical characteristics, and uncertain nonlinear interactions between subsystems are regarded as the stochastic total disturbance (extended state) of each subsystem of the plant. The constant gain ESO and time-varying gain ESO are designed for the estimation of not only the unmeasured state but also the stochastic total disturbance of each subsystem in real time, and the corresponding mean square convergence of these two classes of ESOs are developed rigorously. Some numerical simulations are presented to demonstrate the effectiveness of estimation by ESO approach and the peaking value reduction by the time-varying gain ESO.