Wavelet reduced order observer based adaptive tracking control for a class of uncertain nonlinear systems using reinforcement learning

This Paper investigates the mean to design the reduced order observer and observer based controllers for a class of uncertain nonlinear system using reinforcement learning. 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. 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. Owing to their superior learning capabilities, wavelet networks are employed in this work for the purpose of identification of unknown system dynamics. Using the feedback control, based on reconstructed states, the behavior of closed loop system is investigated. By Lyapunov approach, the uniformly ultimate boundedness of the closed-loop tracking error is verified. A numerical example is provided to verify the effectiveness of theoretical development.