A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems |
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Authors: | Zhang Hua-Guang Zhao Yan Yu Wen and Yang Dong-Sheng |
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Institution: | [1]School of Information Science and Engineering, Northeastern University, Shenyang 110004, China; [2]Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang 110004, China; [3]Department of Automatic Control Engineering, Shenyang Institute of Engineering, Shenyang 110136, China; [4]Departamento de Control Automatico, CINVESTAV-IPN, Av. IPN 2508, Mexico D.F. 07360, Mexico |
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Abstract: | In this paper, a Takagi--Sugeno (T--S) fuzzy model-based method is
proposed to deal with the problem of synchronization of two
identical or different hyperchaotic systems. The T--S fuzzy models
with a small number of fuzzy IF--THEN rules are employed to
represent many typical hyperchaotic systems exactly. The benefit of
employing the T--S fuzzy models lies in mathematical simplicity of
analysis. Based on the T--S fuzzy hyperchaotic models, two fuzzy
controllers are designed via parallel distributed compensation (PDC)
and exact linearization (EL) techniques to synchronize two identical
hyperchaotic systems with uncertain parameters and two different
hyperchaotic systems, respectively. The sufficient conditions for
the robust synchronization of two identical hyperchaotic systems
with uncertain parameters and the asymptotic synchronization of two
different hyperchaotic systems are derived by applying the Lyapunov
stability theory. This method is a universal one of synchronizing
two identical or different hyperchaotic systems. Numerical examples
are given to demonstrate the validity of the proposed fuzzy model
and hyperchaotic synchronization scheme. |
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Keywords: | hyperchaotic synchronization fuzzy modelling T--S fuzzy model exact linearization (EL) |
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