Variable Neural Networks for Nonlinear Adaptive Control

Abstract

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks, A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlineanties of dynamical systems. In 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 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 t.he widths of the Gaussian radial basis functions in the variable neural network are analyslzed to make a compromise between orthogonality and smoothness. The weight adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modelling errors. The tracking errors converge to the required accuracy through the adaptive control algonthm denved by combmmg the vanable neural network and Lyapunov synthesis techniques.