Interval Type-2 Takagi-Sugeno Fuzzy Modeling of the Chaotic Systems Based on Variations in Initial Conditions

Abstract

Chaotic systems are nonlinear dynamic systems, the main feature of which is high sensitivity to initial conditions. To initiate a design process in fuzzy model, chaotic systems must first be represented by T-S fuzzy models. In this paper, a new fuzzy modeling method based on sector nonlinearity approach has been recommended for chaotic systems relating to initial condition variations using the interval type-2 Takagi–Sugeno (IT2 T-S) fuzzy model. Examining many famous chaotic systems, it can be seen that nonlinear terms in chaotic systems are composed of just one variable or more. In the process of constructing an IT2 T-S fuzzy model which represents the chaotic systems, authors will focus on nonlinear terms of the chaotic systems. The proposed interval type-2 Takagi-Sugeno fuzzy modeling method is employed for two kinds of nonlinear terms; at first, a uni-variable nonlinear term is presented and then a multi-variable one will be introduced. So, it will be shown how many famous chaotic systems are represented by IT2 T-S fuzzy model. Then the proposed approach is applied to Genesio-Tesi and Rossler systems. Numerical simulations are given to demonstrate the efficiency of the proposed method in MATLAB environment.