Recursive Estimation of the Takagi-Sugeno Models I: Fuzzy Clustering and the Premise Membership Functions Estimation

Abstract

Fuzzy modelling is an approximation of nonlinear systems by a finite collection of linear systems. On this concept Takagi-Sugeno fuzzy models are based. The procedure for identification of these models include two steps: (a) estimation of membership functions, (b) model parameter estimation. In this paper only the step (a) is considered, where GustafsonKessel clustering algorithm is used. The algorithm detects clusters of different shapes. Parameter estimation of the premise membership function is based on the implementation of recursive least squares algorithm. Based on the obtained clusters, recursive least squares algorithm estimates parameters of membership functions. In this paper, it is assumed that the membership functions have triangular shape, performances of the proposed algorithm are demonstrated by simulation.