Recursive clustering based on a Gustafson-Kessel algorithm

In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented. The presented method combines a recursive Gustafson–Kessel clustering algorithm and the fuzzy recursive least squares method. The on-line Gustafson–Kessel clustering method is derived. The recursive equations for fuzzy covariance matrix, its inverse and cluster centers are given. The use of the method is presented on two examples. First example demonstrates the use of the method for monitoring of the waste water treatment process and in the second example the method is used to develop an adaptive fuzzy predictive functional controller for a pH process. The results for the Mackey–Glass time series prediction are also given.