Control of a class of nonlinear uncertain systems by combining state observers and parameter estimators

The main purpose of this paper is to study the control problem for a class of SISO affine nonlinear systems with unknown dynamics by combining the extended state observer (ESO) technique and the projected gradient estimator. While ESO can be used to estimate the total uncertainties, the projected gradient algorithm is used to estimate the nonparametric uncertainties treated as time-varying parameters. This method improves the traditional active disturbance rejection control (ADRC) technique. It overcomes the difficulty that the traditional ADRC needs to have a “good” estimate for the uncertainties in the input channel. Closed loop stability is proven and the control performance is also analyzed.