Active Disturbance Rejection Control Approach to Output-Feedback Stabilization of MIMO Systems with Stochastic Uncertainty

In this paper, the active disturbance rejection control (ADRC) approach is applied to output-feedback stabilization for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameters from their nominal values. The stochastic total disturbance is then compensated in the feedback loop. As a result, we prove theoretically the mean square practical stability for the closed-loop system with constant gain ESO. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.