This Paper investigates the mean to design the reduced order observer and observer based controllers for a class of delayed uncertain nonlinear system subjected to actuator saturation. A new design approach of wavelet based adaptive reduced order observer is proposed. The proposed wavelet adaptive reduced order observer performs the task of identification of unknown system dynamics in addition to the reconstruction of states of the system. Wavelet neural network (WNN) is used to approximate the uncertainties present in the system as well as to identify and compensate the nonlinearities introduced in the system due to actuator saturation. Using the feedback control, based on reconstructed states, the behavior of closed loop system is investigated. In addition robust control terms are also designed to attenuate the approximation error due to WNN. Adaptation laws are developed for the online tuning of the wavelet parameters and the stability of the overall systems is assured by using the Lyapunov- Krasovskii functional. A numerical example is provided to verify the effectiveness of theoretical development.

This paper is concerned with the observer designing problem for a class of uncertain delayed nonlinear systems using reinforcement learning. Reinforcement learning is used via two Wavelet Neural networks (WNN), critic WNN and action WNN, which are combined to form an adaptive WNN controller. The “strategic” utility function is approximated by the critic WNN and is minimized by the action WNN. Adaptation laws are developed for the online tuning of wavelets parameters. By Lyapunov approach, the uniformly ultimate boundedness of the closed-loop tracking error is verified. Finally, a simulation example is shown to verify the effectiveness and performance of the proposed method.