Direct Adaptive Neural Control of Uncertain Pure-Feedback Systems with Tracking Accuracy Known a Priori via Backstepping Design

Abstract

This paper concerns the adaptive neural network tracking control problem for a class of uncertain pure-feedback nonlinear systems. The main features of the proposed control scheme are shown here and compared to those of existing uncertain pure-feedback systems. First, the accuracy of the ultimate tracking error is given a priori. However, the tracking accuracy of the system cannot be determined a priori if existing control methods are used. Second, unlike in the case of traditional adaptive neural network control systems, the convergence of the tracking error was here analyzed using Barbalat's lemma based on nonnegative functions rather than Lyapunov functions. Third, with help from two novel nth-order continuously differentiable switching functions, the ultimate tracking error can be proven to reach accuracy given a priori and all closed-loop signals are uniformly ultimately bounded. Finally, a simulation is provided to illustrate the effectiveness of the proposed control approach.