Design Of Obf-ts Fuzzy Models Based On Multiple Clustering Validity Criteria

Takagi-Sugeno Fuzzy Models within the framework of Orthonormal Basis Functions (OBF-TS Fuzzy Models) have shown to be an effective approach to nonlinear system identification and control due to several advantages they exhibit over those dynamic model topologies most commonly adopted in the literature. Despite all the theoretical advances and encouraging application results obtained so far, the automatic determination of the number of local OBF models remains an issue. This paper elaborates on the use of a mixture of clustering validity criteria to automatically determine the number of local models based on product space fuzzy clustering of I/O data. © 2007 IEEE.2336339Babuška, R., (1998) Fuzzy Modeling for Control, , KluwerBezdek, J.C., Pal, N.R., Some new indexes of cluster validity (1998) IEEE Trans. on Systems, Man and Cybernetics B, 28 (3), pp. 301-315Campello, R.J.G.B., Hruschka, E.R., A fuzzy extension of the silhouette width criterion for cluster analysis (2006) Fuzzy Sets and Systems, 157, pp. 2858-2875R. J. G. B. Campello, L. A. C. Meleiro, W. C. Amaral, and R. M. Filho. Identification of a bioprocess using Laguerre function based models. In World Congress of Chemical Engineering, page CD, Melbourne, Australia, 2001R. J. G. B. Campello, L. A. C. Meleiro, and W. C. Amaral. Takagi-sugeno fuzzy models within orthonormal basis function framework and their application to process control. In IEEE Int. Conf. Fuzzy Systems, pages 1399-1404, Honolulu, USA, 2002R. J. G. B. Campello, L. A. C. Meleiro, and W. C. Amaral. Control of a bioprocess using orthonormal basis function fuzzy models. In IEEE Int. Conf. Fuzzy Systems, pages 801-806, Budapest, Hungary, 2004Campello, R.J.G.B., Von Zuben, F.J., Amaral, W.C., Meleiro, L.A.C., Maciel Filho, R., Hierarchical fuzzy models within the framework of orthonormal basis functions and their application to bioprocess control (2003) Chemical Engineering Science, 58, pp. 4259-4270Heuberger, P.S.C., Van den Hof, P.M.J., Wahlberg, B., (2005) Modelling and Identification with Rational Orthogonal Basis Functions, , SpringerHöppner, F., Klawonn, F., Kruse, R., Runkler, T., (1999) Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition, , John Wiley & SonsMedeiros, A.V., Amaral, W.C., Campello, R.J.G.B., GA optimization of generalized OBF TS fuzzy models with global and local estimation approaches (2006) Proc. IEEE Int. Conf. Fuzzy Systems, pp. 8494-8501. , Vancouver, CanadaMedeiros, A.V., Amaral, W.C., Campello, R.J.G.B., GA optimization of OBF TS fuzzy models with linear and non linear local models (2006) Proc. Brazilian Symposium on Neural Networks, , Ribeirão Preto, BrazilMedeiros, A.V., (2006) Modeling of Nonlinear Dynamic Systems using Fuzzy Systems, Genetic Algorithms and Orthonormal Basis Functions, , Master's Degree Thesis, School of Electrical and Computer Engineering FEEC, UNICAMP, Brazil, Jan, In PortugueseNelles, O., (2001) Nonlinear System Identification, , Springer-VerlagG. H. C. Oliveira, R. J. G. B. Campello, and W. C. Amaral. Fuzzy models within orthonormal basis function framework. In IEEE Int. Conf. Fuzzy Systems, pages 957-962, Seoul, Korea, 1999Johansen, R.S.T.A., Murray-Smith, R., On the interpretation and identification of dynamic takagi-sugeno fuzzy models (2000) IEEE Transactions on Fuzzy Systems, 8 (3), pp. 297-31