Control of uncertain nonlinear systems based on observers and estimators

In this paper, we consider a class of nonlinear dynamical systems with zero dynamics, which is subject to both unknown nonparametric dynamics and external disturbances, and is required to track a given reference signal by using the output feedback. Our controller is designed based on both the extended state observer (ESO) and the projected gradient estimator. While the ESO is used to estimate the total uncertainties, the projected gradient algorithm is used to estimate the nonparametric uncertainties treated as “time-varying parameters”. This method overcomes the difficulties that the traditional active disturbance rejection control (ADRC) technique needs to have a “good” prior estimate for the uncertainties in the input channel. The closed-loop system is shown to be semi-globally stable, and at the same time, the tracking error can be made arbitrarily small.