Robust Kernel Clustering Algorithm for Nonlinear System Identification

Mohamed Bouzbida,Lassad Hassine,Abdelkader Chaari

doi:10.1155/2017/2427309

Abstract

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 C-Means (FCM) algorithm, Possibilistic C-Means (PCM) algorithm, and Possibilistic Fuzzy C-Means (PFCM) algorithm. This paper presents a new clustering algorithm for Takagi-Sugeno fuzzy model identification. Our proposed algorithm called Robust Kernel Possibilistic Fuzzy C-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.

Highlights

Modeling and identification are significant steps in the design of the control system
We propose a new clustering algorithm called Robust Kernel Possibilistic Fuzzy C-Means (RKPFCM), which adopts a kernel induced metric in the data space to replace the original Euclidean norm metric
To identify the premise parameters of a Takagi-Sugeno fuzzy model described by equation (1), we used the Possibilistic Fuzzy C-Means (PFCM) algorithm and our proposed algorithms (RKPFCM and RKPFCM-Particle Swarm Optimization (PSO))

Summary

Introduction

Modeling and identification are significant steps in the design of the control system. The identification problem consists of estimating the model parameters In this context, to identify the parameters of Takagi-Sugeno fuzzy model, many techniques were developed such as the Adaptive schemes, heuristic approaches, nearest neighbor clustering, and support vector learning mechanisms. Noise in the data sets can make the situation worse by creating many inauthentic minima These are able to distort the global minimum solution found by FCM algorithm. The PCM algorithm is robust against the noise points and allows identifying these outliers, it is very responsive to initializations and occasionally generates coincident clusters. To solve this deficiency of identical clusters, a Possibilistic Fuzzy c-Means (PFCM) algorithm was suggested by Wu and Zhou in 2006.

Takagi-Sugeno Fuzzy Model

Identification Algorithm for Premise Parameters

Identification for Consequent Parameters

Simulation Results and Validation Model

Conclusion