Identification and Analysis of MIMO Systems based on Clustering Algorithm

Abstract

This paper presents a compact Takagi-Sugeno fuzzy model that can be effectively used to represent MIMO dynamical systems. For the identification of this model a modified Gath-Geva fuzzy clustering algorithm has been developed. The case studies demonstrate that the proposed algorithm can be a useful and effective tool to select the embedding dimension of a dynamical system. This is a key step toward the analysis and prediction of nonlinear and chaotic time-series. The clustering is applied in the reconstruction space defined by the lagged output variables. The main advantage of the proposed solution is that three tasks are simultaneously solved during clustering: selection of the embedding dimension, estimation of the intrinsic (local) dimension, and identification of a model that can be used for prediction. The results were excellent in the case of the analyzed, three and four dimensional systems. Programs and data sets will be available via Internet on our web page http://www.fmt.vein.hu/softcomp/timeseries.