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

• Published in: Journal of theoretical and applied physics Vol. 8; no. 1; pp. 1 - 10
• Main Authors: Hasanifard, Goran, Gharaveisi, Ali Akbar, Vali, Mohammad Ali
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2014; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Chaos theory; Condensed Matter Physics; Dynamical systems; Fuzzy; Fuzzy logic; Fuzzy set theory; Intervals; Mathematical models; Medical and Radiation Physics; Molecular; Nanoscale Science and Technology; Optical and Plasma Physics; Physics; Physics and Astronomy; Uncertainty; Footprint of uncertainty; Lower and upper membership functions; Parametric uncertainty; Interval type-2 Takagi–Sugeno fuzzy system; Chaotic systems
• ISSN: 1735-9325; 2251-7227; 2251-7235
• DOI: 10.1007/s40094-014-0115-y

A motivation for using fuzzy systems stems in part from the fact that they are particularly suitable for processes when the physical systems or qualitative criteria are too complex to model and they have provided an efficient and effective way in the control of complex uncertain nonlinear systems. To realize a fuzzy model-based design for chaotic systems, it is mostly preferred to represent them by T–S fuzzy models. In this paper, a new fuzzy modeling method has been introduced for chaotic systems via the interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy model. An IT2 fuzzy model is proposed to represent a chaotic system subjected to parametric uncertainty, covered by the lower and upper membership functions of the interval type-2 fuzzy sets. Investigating many well-known chaotic systems, it is obvious that nonlinear terms have a single common variable or they depend only on one variable. If it is taken as the premise variable of fuzzy rules and another premise variable is defined subject to parametric uncertainties, a simple IT2 T–S fuzzy dynamical model can be obtained and will represent many well-known chaotic systems. This IT2 T–S fuzzy model can be used for physical application, chaotic synchronization, etc. The proposed approach is numerically applied to the well-known Lorenz system and Rossler system in MATLAB environment.