An Identification System Design Using a CMAC with a Learning Algorithm Based on the Kalman Filter

Abstract

Abstract The Cerebellar Model Arithmetic Computer (CMAC) proposed by Albus is a neural network that imitates the human cerebellum, and it is basically a table lookup technique for representing nonlinear functions. The CMAC can approximate a wide variety of nonlinear functions by learning. However, the CMAC requires a number of learning iterations to achieve the adequate approximation accuracy, because CMAC learning algorithm is based on the Least Mean Square method. In this paper, a CMAC learning algorithm based on the Kalman filter is proposed. Using this algorithm, the number of learning iterations is reduced, and the comparable approximation accuracy is achieved as compared to the system using conventional learning algorithm. Generally, the learning algorithm based on the Kalman filter requires much larger computational quantity than that required by algorithms based on the Least Mean Square method. For CMAC system equations contain a sparse matrix, the computational quantity of the proposed learning algorithm can be reduced. Furthermore, since two CMAC weights being in the far place from each other can be considered to have little correlation, the number of weights that should be updated for an learning iteration can be reduced. This reduces the computational quantity of the learning algorithm. Computer simulation results for the modeling problems are presented.