Optimization of Gaussian Membership Functions using Unscented Kalman Filter

Fuzzy systems are popular in the modelling of nonlinear systems. The shape and parameters defining the membership function have a significant effect on performance of the fuzzy model. Thus the study of tuning of membership functions according to the specific system under consideration is of great importance. Two of the existing methods for membership function adjustments are mainly based on Kalman filter and Extended Kalman filter (EKF) on triangular membership functions. They are prone to linearization error and hence perform poorly on non-linear systems. We propose a method to adjust Gaussian membership functions using Unscented Kalman filter (UKF). The comparisons of the simulated fuzzy control system using triangular and Gaussian membership functions adjusted using EKF and UKF shows that Gaussian curves can lead to faster stabilization and increased performance of the system.