No abstract

No abstract

Many clustering algorithms have been proposed in literature to identify the parameters involved in the Takagi–Sugeno fuzzy model, we can quote as an example the Fuzzy C-Means algorithm (FCM), the Possibilistic C-Means algorithm (PCM), the Allied Fuzzy C-Means algorithm (AFCM), the NEPCM algorithm and the KNEPCM algorithm. The main drawback of these algorithms is the sensitivity to initialization and the convergence to a local optimum of the objective function. In order to overcome these problems, the particle swarm optimization is proposed. Indeed, the particle swarm optimization is a global optimization technique. Thus, the incorporation of local research capacity of the KNEPCM algorithm and the global optimization ability of the PSO algorithm can solve these problems. In this paper, a new clustering algorithm called KNEPCM-PSO is proposed. This algorithm is a combination between Kernel New Extended Possibilistic C-Means algorithm (KNEPCM) and Particle Swarm Optimization (PSO). The effectiveness of this algorithm is tested on nonlinear systems and on an electro-hydraulic system.

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.