Design of an On-Line Recurrent Wavelet Network Controller for a Class of Nonlinear Systems

This paper investigate a simple structure of recurrent wavelet neural network (RWNN) for on-line control of a class of nonlinear dynamic systems. The RWNN combines the properties of recurrent neural network (RNN) such as storage of past information of the network and the basic ability of wavelet neural network (WNN) such as the fast convergence and localization properties. The proposed controller has a simple structure and it is trained as on-line in closed loop system. The real time recurrent learning (RTRL) algorithm is applied to adjust the shape of wavelet functions and the connection weights. Finally, the RWNN controller is applied to two control problems. A disturbance is also added to the system to show disturbance rejection property. Simulation results verify that a favorable tracking response can be achieved by the RWNN controller even with the presence of disturbance and the change of parameters of the system. The proposed controller despite the simple structure is able to control a class of nonlinear dynamic systems.