Modified Gath-Geva clustering based linear T-S fuzzy model identification for multi-input multi-output chaotic systems

A modified Gath-Geva clustering based linear T-S fuzzy model identification method for multi-input multi-output chaotic systems is proposed. Noise reduction via local projection and derivatives of state variable estimation using Heirmit spline interpolation are performed at first for better data. Then initial linear T-S fuzzy model is derived using modified Gath-Geva clustering, whose rule number is optimized by clustering validation procedure. After clustering, model reduction is implemented using OLS (Orthogonal Least Squares) and modified Fischer´s interclass separability criteria in order to obtain compact and transparent model. Parameters of the reduced fuzzy model are optimized by constraint Levenberg-Marquardt method to improve its precision, while preserving its interpretability. Simulation results show the efficiency of proposed method.