Identification of the Henon chaotic map by fuzzy modeling and Nelder-Mead simplex method

Identification of the Henon chaotic map by fuzzy modeling and Nelder-Mead simplex method

Author Coelho, Leandro dos Santos Google Scholar
Araujo, Ernesto Autor UNIFESP Google Scholar
Institution Natl Inst Space Res INPE
Pontifical Catholic Univ Parana
Universidade Federal de São Paulo (UNIFESP)
Hosp Municipal Dr Jose de Carvalho Florence
Associacao Paulista Desenvolvimento Med SPDM
Abstract A nonlinear identification approach for describing the dynamical behavior of a Henon chaotic map based on Nelder-Mead simplex method and Takagi-Sugeno (T-S) fuzzy model is proposed in this paper. Nonlinear dynamic systems exhibiting chaotic behavior arise in real world problems in many areas of science and technology. the investigation of such systems becomes further attractive since they are simple systems able to imitate the behavior of complex systems. An alternative to approximate a nonlinear system is to employ fuzzy models since they are universal approximators able to adequately approximate any continuous functions to an arbitrary precision. Due to that it became a powerful tool for the nonlinear identification and control. Another advantage of using T-S fuzzy modeling is its characteristic of representing a highly nonlinear functional relation with a small number of rules. Nelder-Mead simplex method is proposed here as the method for optimizing the premise part while least mean squares technique is employed for consequent part of production rules of a T-S fuzzy model. Numerical results indicate that the description of discrete chaotic dynamics of Henon map can be accomplished by exploring the effectiveness of NMO approach combined with T-S fuzzy modeling in constructing an appropriate nonlinear identification. (C) 2008 Elsevier B.V. All rights reserved.
Language English
Sponsor Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Grant number CNPq: 309646/2006-5/PQ
Date 2009-09-15
Published in Chaos Solitons & Fractals. Oxford: Pergamon-Elsevier B.V., v. 41, n. 5, p. 2762-2772, 2009.
ISSN 0960-0779 (Sherpa/Romeo, impact factor)
Publisher Elsevier B.V.
Extent 2762-2772
Access rights Closed access
Type Article
Web of Science ID WOS:000268460600079

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