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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 2427309, 11 pages
Research Article

Robust Kernel Clustering Algorithm for Nonlinear System Identification

1National Higher Engineering School of Tunis (ENSIT), University of Tunis, 5 Av. Taha Husein, BP 56, 1008 Tunis, Tunisia
2Laboratoire d’Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), University of Tunis, ENSIT, Tunis, Tunisia

Correspondence should be addressed to Mohamed Bouzbida; rf.liamtoh@demahom_adibzuob

Received 12 December 2016; Revised 16 March 2017; Accepted 30 March 2017; Published 14 May 2017

Academic Editor: Francisco Gordillo

Copyright © 2017 Mohamed Bouzbida et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In engineering field, it is necessary to know the model of the real nonlinear systems to ensure its control and supervision; in this context, fuzzy modeling and especially the Takagi-Sugeno fuzzy model has drawn the attention of several researchers in recent decades owing to their potential to approximate nonlinear behavior. To identify the parameters of Takagi-Sugeno fuzzy model several clustering algorithms are developed such as the Fuzzy -Means (FCM) algorithm, Possibilistic -Means (PCM) algorithm, and Possibilistic Fuzzy -Means (PFCM) algorithm. This paper presents a new clustering algorithm for Takagi-Sugeno fuzzy model identification. Our proposed algorithm called Robust Kernel Possibilistic Fuzzy -Means (RKPFCM) algorithm is an extension of the PFCM algorithm based on kernel method, where the Euclidean distance used the robust hyper tangent kernel function. The proposed algorithm can solve the nonlinear separable problems found by FCM, PCM, and PFCM algorithms. Then an optimization method using the Particle Swarm Optimization (PSO) method combined with the RKPFCM algorithm is presented to overcome the convergence to a local minimum of the objective function. Finally, validation results of examples are given to demonstrate the effectiveness, practicality, and robustness of our proposed algorithm in stochastic environment.