Training fuzzy systems with the extended Kalman %lter

The generation of membership functions for fuzzy systems is a challenging problem. We show that for Mamdani-type fuzzy systems with correlation-product inference, centroid defuzzi%cation, and triangular membership functions, optimizing the membership functions can be viewed as an identi%cation problem for a nonlinear dynamic system. This identi%cation problem can be solved with an extended Kalman %lter. We describe the algorithm and compare it with gradient descent and with adaptive neuro-fuzzy inference system (ANFIS) based optimization of fuzzy membership functions. The methods discussed in this paper are illustrated on a fuzzy %lter for motor winding current estimation, and are compared with Butterworth %ltering. We demonstrate that the Kalman %lter can be an e6ective tool for improving the performance of a fuzzy system. c © 2001 Elsevier Science B.V. All rights reserved.