Variable Neural Networks for Adaptive Control of Nonlinear Systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, is referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time according to specified design strategies so that the network will not overfit or underfit the the data set. Based on the Gaussian radial basis function variable neural network, an adaptive control scheme is presented. The location of the centres and the determination of the widths of the Gaussian radial basis functions in the variable neural network are analysed to make a compromise between orthogonality and smoothness. The weight of adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modelling error. The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using a simulated example.