Prediction and identification using recurrent wavelet-based cerebellar model articulation controller neural networks

A recurrent wavelet-based cerebellar model articulation controller (RWCMAC) neural network used for solving the prediction and identification problem is proposed in this paper. The proposed RWCMAC has superior capability to the conventional cerebellar model articulation controller (CMAC) neural network in efficient learning mechanism, guaranteed system stability and dynamic response. The recurrent network is embedded in the RWCMAC by adding feedback connections in the mother wavelet association memory space so that the RWCMAC captures the dynamic response, where the feedback units act as memory elements. The dynamic gradient descent method is adopted to adjust RWCMAC parameters on-line. Moreover, the analytical method based on a Lyapunov function is proposed to determine the learning-rates of RWCMAC so that the variable optimal learning-rates are derived to achieve most rapid convergence of identifying error. Finally, the RWCMAC is applied in two computer simulations. Simulation results show that accurate identifying response and superior dynamic performance can be obtained because of the powerful on-line learning capability of the proposed RWCMAC.

I. Introduction

RECENTYL, many researches have been done on the applications of neural networks (NNs) for prediction, identification and control of dynamic systems [1]–[5]. The most useful property of NNs is their ability to approximate arbitrary linear or nonlinear mapping through learning. Based on their approximation ability, the NNs have been used for approximation of control system dynamics or controllers. According to the structure, the NNs can be mainly classified as feedforward neural networks (FNNs) [2], [3] and recurrent neural networks (RNNs) [4], [5]. RNN has capabilities superior to FNN, such as the dynamic response and information storing ability [4], [5]. Since a RNN has an internal feedback loop, it captures the dynamic response of system with external feedback through delays. Thus, the RNN is a dynamic mapping and demonstrates good control performance in presence of unmodelled dynamics. However, no matter FNNs or RNNs, the learning is slow since all the weights are updated during each learning cycle. Therefore, the effectiveness of NN is limited in problems requiring on-line learning.