Robust fuzzy Gustafson–Kessel clustering for nonlinear system identification

Abstract

This paper deals with Takagi–Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson–Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input–output data. The EGK algorithm can automatically determine the ‘optimal’ number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally-weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.