Wavelet Reduced Order Observer Based Adaptive Tracking Control for a Class of Uncertain Multiple Time Delay Nonlinear Systems Subjected to Actuator Saturation Using Actor Critic Architecture

Abstract

This Paper investigates the mean to design the reduced order observer and observer based controller for a class of uncertain delayed nonlinear system subjected to actuator saturation using Actor Critic architecture. A new design approach of wavelet based adaptive reduced order observer is proposed. The task of the proposed wavelet adaptive reduced order observer is to identify the unknown system dynamics and to reconstruct the states of the system. Wavelet neural network (WNN) is implemented 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. Reinforcement learning is applied through Actor-Critic architecture where a separate structure is for both perception (critic) and action (actor). 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 critic WNN approximates the “strategic” utility function which is then minimized by the action WNN. Using the feedback control, based on reconstructed states, the behavior of closed loop system is investigated. By Lyapunov-Krasovskii approach, the closed-loop tracking error is proved to be uniformly ultimate bounded. A numerical example is provided to verify the effectiveness of theoretical development.