Training fuzzy systems with the extended Kalman filter

7 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 9 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 11 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 13 ltering. We demonstrate that the Kalman lter can be an e6ective tool for improving the performance of a fuzzy system. c © 2002 Published by Elsevier Science B.V. 15