Fuzzy modeling for chaotic systems via interval type-2 T–S fuzzy model with parametric uncertainty

A motivation for using fuzzy systems stems inpart from the fact that they are particularly suitable forprocesses when the physical systems or qualitative criteriaare too complex to model and they have provided an efficientand effective way in the control of complex uncertainnonlinear systems. To realize a fuzzy model-based designfor chaotic systems, it is mostly preferred to represent themby T–S fuzzy models. In this paper, a new fuzzy modelingmethod has been introduced for chaotic systems via theinterval type-2 Takagi–Sugeno (IT2 T–S) fuzzy model. AnIT2 fuzzy model is proposed to represent a chaotic systemsubjected to parametric uncertainty, covered by the lowerand upper membership functions of the interval type-2fuzzy sets. Investigating many well-known chaotic systems,it is obvious that nonlinear terms have a singlecommon variable or they depend only on one variable. If itis taken as the premise variable of fuzzy rules and anotherpremise variable is defined subject to parametric uncertainties,a simple IT2 T–S fuzzy dynamical model can beobtained and will represent many well-known chaoticsystems. This IT2 T–S fuzzy model can be used forphysical application, chaotic synchronization, etc. Theproposed approach is numerically applied to the wellknownLorenz system and Rossler system in MATLABenvironment.