New Adaptive Neural Network for Uncertain Nonlinear System with Disturbance

Abstract

Abstract-The paper deals with the problem of tracking control for a class of nonlinear systems in presence of the disturbances. The developed formation for the tracking control is taken into account as an adaptive neural network. The set of controller's parameter, which is a satisfy Hurwitz polynomial, is then updated by adaptive laws via a model reference system. In addition, the unknown nonlinear functions are estimated by radial basis functions neural network. The adaptive updated law based on radial basis functions neural network and a feed-forward correction is proposed to estimate both estimation errors of nonlinear functions and external disturbances, which is called lumped disturbances. The feed-forward correction term is calculated by the algebraic equation regarding the parameters of controller and the radial basis function. Moreover, this estimator (using estimating the lumped disturbance) is also used both in class of SISO nonlinear and MIMO nonlinear system. Thanks to Lyapunov's theory, asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, two examples of coupled tank liquid system and an active magnetic bearing system, are presented to illustrate the our proposed methods.