Output Tracking for MIMO Nonlinear Systems Under Stochastic Disturbances via a Homogeneous Nonlinear Extended State Observer

ABSTRACT In this paper, we investigate output regulation for a class of multi‐input multi‐output (MIMO) nonlinear systems subjected to colored noises and bounded noises, employing the active disturbance rejection control (ADRC) approach. To tackle this problem, we develop a homogeneous nonlinear extended state observer (ESO) that can estimate both unmeasurable states and the stochastic total disturbance, encompassing colored noises and bounded noise, for each subsystem. By utilizing these estimates, the system is approximately decoupled after the stochastic total disturbance is eliminated from the feedback loop. Based on the homogeneous nonlinear ESO and nonlinear functions that adhere to Hölder continuity, we design an output feedback control. We establish the existence of global weak solutions for the closed‐loop system without necessitating the global Lipschitz condition for the involved nonlinear functions. Moreover, we illustrate that, with identical tuning parameters, the estimation error precision and tracking convergence accuracy of our proposed method outperform those of a linear ESO. To substantiate the practicality of our control strategy, we conduct a sequence of numerical simulations on the free‐body model of a 2‐degree‐of‐freedom helicopter.