Adaptive Asymptotic Tracking Control of a Class of Discrete-Time Nonlinear Systems with Parametric and Nonparametric Uncertainties

In this paper, adaptive control is studied for a class of nonlinear discrete-time systems in parameter-strict-feedback form with both parametric and non-parametric uncertainties. The non-parametric uncertainty function is assumed to satisfy the Lipschitz condition. To achieve asymptotical tracking performance, estimation of both uncertainties is constructed. Future states are predicted to overcome the noncausal problem. Based on future states prediction and uncertainties estimation, a novel adaptive control is proposed. An augmented tracking error of equal growth order of the output tracking error is used in the parameter estimation law. The proposed adaptive control achieves asymptotical tracking performance and guarantees the boundedness of all closed-loop signals. The effectiveness of the proposed control law is demonstrated in the simulation.