Robust neural tracking controller design for a class of discrete-time nonlinear systems under arbitrary switching

Abstract

In this article, the problem of robust tracking control is investigated for a class of discrete-time switched nonlinear uncertain system in strict-feedback form, and a novel robust neural tracking control scheme through backstepping technique is proposed for the first time. In order to handle the problem of causality contradiction, the original discrete-time nonlinear switched system is transformed into a special maximum n-step ahead predictor which suits the application of backstepping technique. The radial basis function(RBF) neural networks are adopted to approximate the unknown lumped function at the last step of backstepping procedure, not necessary to approximate all the virtual control laws at each intermediate step. Thus, the process of controller design is significantly simplified in contrast with the existing results. The stability analysis proves the proposed approach guarantees the semi-globally uniformly ultimately bounded(SGUUB) of the closed-loop system, and the tracking error asymptotically converges to an arbitrarily small neighborhood of origin by appropriately designing control parameters. Finally, simulation results are provided to demonstrate the correctness and effectiveness of the proposed scheme.