Training fuzzy systems with the extended Kalman filter

Abstract

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 defuzziÿcation, and triangular membership functions, optimizing the membership functions can be viewed as an identiÿcation problem for a nonlinear dynamic system. This identiÿcation problem can be solved with an extended Kalman ÿlter. 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 ÿlter for motor winding current estimation, and are compared with Butterworth ÿltering. We demonstrate that the Kalman ÿlter can be an e ective tool for improving the performance of a fuzzy system.

Cardiomyopathy Detection from Electrocardiogram Features

“…Gradient descent can be further improved by using an adaptive learning rate and momentum term (Nauck, Klawonn, Kruse, 1997). Kalman filtering is a gradient-based method that can give better fuzzy system and neural network training results than gradient descent (Simon, 2002a(Simon, , 2002b. Constrained Kalman filtering can further improve fuzzy system results by optimally constraining the network parameters (Simon, 2002c).…”

Review of Hybridizations of Kalman Filters with Fuzzy and Neural Computing for Mobile Robot Navigation

“…EKF improves over gradient descent because it introduces an adaptive learning gain (the Kalman gain) depending on the uncertainty of the network prediction, thus ensuring smooth convergence. The EKF has been also applied to tuning the membership functions in Mamdani type of fuzzy systems with correlation inference [19]. There the estimation of the optimal membership parameters is found equivalent to nonlinear dynamic system identification problem, solved applying the EKF.…”

Chaotic Ant Swarm Designed T-S Fuzzy System for Adaptive Control of Dynamical Systems

“…Overall, all the existing training algorithms can be classified into derivative-based and derivativefree algorithms. The derivative-based methods include backpropagation algorithm (Wang, 1992a), simplex method (Egusa, 1995), least squares (Wang, 1992b), adaptive learning algorithm (Lin, 1999) and the extended Kalman filter method (Simon, 2002), etc. Derivativebased methods require that the objective function must have the derivative and tend to converge to local minima.…”

“…Derivativebased methods require that the objective function must have the derivative and tend to converge to local minima. They are limited to specific objective functions, specific types of inference, and specific types of membership functions (Simon, 2002). The derivative-free methods that have been used include clustering algorithm (Chen, 1998), neural network (Figueiredo, 1999), genetic algorithm (Chen, 2003), cell mapping (Smith, 1991), fuzzy equivalence relations (Wu, 1999), and inductive learning algorithm (Castro, 1997).…”

“…Derivativefree methods have the advantage that they do not require the derivative of the objective function. They are more robust than derivativebased methods with respect to finding a global minimum and with respect to their applicability to a wide range of objective functions (Simon, 2002).…”