Semi-parametric adaptive control of discrete-time nonlinear systems

In this paper, we investigate a novel adaptive design approach for nonlinear systems as an exploration of the new challenging topic on dealing with both parametric and nonparametric internal uncertainties in adaptive control of discrete-time nonlinear systems. The existence of both two kinds of uncertainties makes it very difficult or even impossible to apply the traditional recursive identification algorithms which are designed for parametric systems. To best utilize the existing adaptive control technique, a novel deadzone with threshold converging to zero has been proposed to modify the traditional gradient update law for parameters estimation, while an auxiliary output including both uncertainties is introduced to facilitate the nonparametric uncertainties compensation. It is rigorously proved that the designed adaptive control guarantees the boundedness of all the closed-loop signals and achieves asymptotic tracking performance.