Further results on adaptive control for a class of nonlinear systems using neural networks

Abstract

Zhang et al. presented an excellent neural-network (NN) controller for a class of nonlinear control designs. The singularity issue is completely avoided. Based on a modified Lyapunov function, their lemma illustrates the existence of an ideal control which is important in establishing the NN approximator. In this note, we provide a Lyapunov function to realize an alternative ideal control which is more direct and simpler. The major contributions of this note are divided into two parts. First, it proposes a control scheme which results in a smaller dimensionality of NN than that of Zhang et al. In this way, the proposed NN controller is easier to implement and more reliable for practical purposes. Second, by removing certain restrictions from the design reported by Zhang et al., we further develop a new NN controller, which can be applied to a wider class of systems.