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.

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Takagi-Sugeno (TS) fuzzy model have received particular attention in the area of nonlinear identification due to their potentialities to approximate any nonlinear behavior [1]. In literature, several fuzzy clustering algorithms have been proposed to identify the parameters involved in the Takagi-Sugeno fuzzy model, as the Fuzzy C-Means algorithm (FCM) and the Allied Fuzzy C-Means algorithm (AFCM). This paper presents the New Allied Fuzzy C-Means algorithm (NAFCM) extension of the AFCM algorithm. Then an optimization method using the Particle Swarm Optimization method (PSO) combined with the NAFCM algorithm is presented in this paper (NAFCM-PSO algorithm).The simulation's results on a nonlinear system shows that the New Allied Fuzzy C-Means algorithm combined with the PSO algorithm gives results more effective and robust than the Allied Fuzzy C-Means algorithm.

The identification of nonlinear systems operating in a stochastic environment is an important problem in various discipline science and engineering. Fuzzy modeling and especially the T-S fuzzy model draw the attention of several researchers in recent decades this is due to their potential to approximate highly nonlinear behavior. An algorithm allowing the identification of the premise and consequent parameters intervening in the T-S fuzzy model at the same time and this starting from the minimization of four optimization criteria is used. A modification on both last optimization criterion is considered. Then an optimization method using the Particle Swarm Optimization method (PSO) is presented in this paper. Particle Swarm Optimization algorithm combined with the proposed algorithm is also presented. Simulation results on a nonlinear system and on a level control system shows that the proposed algorithm combined with the PSO algorithm gives results more effective than the proposed algorithm only more particularly to the level convergence and time computing.

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