New Adaptive Neural Network for Uncertain Nonlinear System with Disturbance

Abstract

An output of RBF neural network depends linearly on the matrix weights, a training is thus a linear optimization problem. However, by adjusting the centers and the widths this type of neural network structure becomes nonlinearly parameterized. In this work, lumped disturbances consisting of both approximation errors and external disturbance are estimated by an adaptive RBF neural network structure combining with a feed-forward correction, in which the feed-forward correction term is calculated by the algebraic equation regarding the parameters of controller and the radial basis function. This estimator (using estimating the lumped disturbance) is also used both in class of SISO nonlinear and MIMO nonlinear system. In addition,  an adaptive scheme for the RBF neural network (an output and n outputs) is developed to approximate unknown system functions. On the other side, the performance of closed loop system (settling time, overshoot and the static error) would be improved by using an adaptive law to update the parameters of controller instead of choosing fixed controller's parameters which are coefficients of hurwitz polynomial. Thanks to Lyapunov's theory, asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, there are two examples, coupled tank liquid system and an active magnetic bearing system, are presented to illustrate the our proposed methods.