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Chin. Phys. B, 2008, Vol. 17(11): 4056-4066    DOI: 10.1088/1674-1056/17/11/019
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A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

Yu Wena, Zhao Yanb, Yang Dong-Shengc, Zhang Hua-Guangd
a Departamento de Control Automatico, CINVESTAV-IPN, Av. IPN 2508, M\'exico D.F. 07360, M\'exico; b Department of Automatic Control Engineering, Shenyang Institute of Engineering, Shenyang 110136, China; c School of Information Science and Engineering, Northeastern University, Shenyang 110004, China; d School of Information Science and Engineering, Northeastern University, Shenyang 110004, China;Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang 110004, China
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.
Keywords:  hyperchaotic synchronization      fuzzy modelling      T--S fuzzy model      exact linearization (EL)  
Received:  09 April 2008      Revised:  06 May 2008      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 60534010, 60572070, 60774048 and 60728307), the Program for Changjiang Scholars and Innovative Research Groups of China (Grant No 60521003), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070145015), and the National High Technology Research and Development Program of China (Grant No 2006AA04Z183).

Cite this article: 

Yu Wen, Zhao Yan, Yang Dong-Sheng, Zhang Hua-Guang A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems 2008 Chin. Phys. B 17 4056

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