Adaptive neural network tracking control for a class of non-linear systems

This article extends the application of the adaptive neural network control to a new class of uncertain MIMO non-linear systems, which are composed of interconnected subsystems where each interconnected subsystem is in the non-affine pure-feedback form. Because both the variables which are used as virtual controllers and the actual controllers appear non-linearly in unknown functions of the MIMO systems, thus, this class of systems is difficult to control. The radial basis function neural networks are utilised to approximate the desired virtual controllers and the desired actual controllers which are obtained by using implicit function theorem. The salient property of the proposed approach is that the number of the adjustable parameters is less than the numerous alternative approaches existing in the literature. It is proven that, under appropriate assumptions, all the signals in the closed-loop system are uniformly bounded and the tracking errors converge to a small neighbourhood of the origin by appropriately choosing design parameters. The feasibility of the developed approach is verified by two simulation examples.