Adaptive Observer Based Tracking Control for a Class of Uncertain Nonlinear Systems with Delayed States and Input Using Self Recurrent Wavelet Neural Network

This paper proposes an observer based adaptive tracking control strategy for a class of uncertain nonlinear systems with delay in state as well as in input. Self recurrent wavelet neural network (SRWNN) is used to approximate the uncertainties present in the system as well as to identify and compensate the dynamic nonlinearities. The architecture of the SRWNN is a modified model of the wavelet neural network (WNN). However, unlike WNN, since a mother wavelet layer of the SRWNN is composed of self feedback neurons, the SRWNN can store the past information of wavelets. In addition robust control terms are also designed to attenuate the approximation error due to SRWNN. Adaptation laws are developed for the online tuning of the wavelet parameters and the stability of the overall system is assured by using the Lyapunov-Krasovskii functional. Finally some simulations are performed to verify the effectiveness and performance of the proposed control scheme.