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RBF neural network based H ∞ synchronization for unknown chaotic systems

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Abstract

In this paper, we propose a new H ∞ synchronization strategy, called a Radial Basis Function Neural NetworkH ∞ synchronization (RBFNNHS) strategy, for unknown chaotic systems in the presence of external disturbance. In the proposed framework, a radial basis function neural network (RBFNN) is constructed as an alternative to approximate the unknown nonlinear function of the chaotic system. Based on this neural network and linear matrix inequality (LMI) formulation, the RBFNNHS controller and the learning laws are presented to reduce the effect of disturbance to an H ∞ norm constraint. It is shown that finding the RBFNNHS controller and the learning laws can be transformed into the LMI problem and solved using the convex optimization method. A numerical example is presented to demonstrate the validity of the proposed RBFNNHS scheme.

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References

  • Ahn C 2009 An H ∞ approach to anti-synchronization for chaotic systems. Phys. Lett. A 373: 1729–1733

    Article  MathSciNet  Google Scholar 

  • Ahn C 2010 Fuzzy delayed output feedback synchronization for time-delayed chaotic systems. Nonlinear Analysis: Hybrid Systems 4: 16–24

    Article  MATH  MathSciNet  Google Scholar 

  • Bai E, Lonngen K 1997 Synchronization of two Lorenz systems using active control. Phys. Rev. E 8: 51–58

    MATH  Google Scholar 

  • Bai E, Lonngren K 2000 Sequential synchronization of two Lorenz systems using active control. Chaos, Solitons and Fractals 11: 1041–1044

    Article  MATH  Google Scholar 

  • Boyd S, Ghaoui L E, Feron E, Balakrishinan V 1994 Linear matrix inequalities in systems and control theory (Philadelphia, PA: SIAM)

    Google Scholar 

  • Chen M, Chen W 2009 Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems. Chaos, Solitons and Fractals 41: 2716–2724

    Article  Google Scholar 

  • Chen M, Jiang C, Jiang B, Wu Q 2009 Sliding mode synchronization controller design with neural network for uncertain chaotic systems. Chaos, Solitons and Fractals 39: 1856–1863

    Article  Google Scholar 

  • Chen M, Jiang C, Wu Q, Chen W 2006 Synchronization scheme for uncertain chaotic systems via rbf neural network. Chin. Phys. Lett. 350: 363–366

    Google Scholar 

  • Chen G, Dong X 1998 From chaos to order (Singapore: World Scientific)

    MATH  Google Scholar 

  • Gahinet P, Nemirovski A, Laub AJ, Chilali M 1995 LMI Control Toolbox (Natik: The Mathworks Inc.)

    Google Scholar 

  • Genesio R, Tesi A 1992 Aharmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28: 531–548

    Article  MATH  Google Scholar 

  • Gupta M M, Jin L, Homma N 2003 Static and dynamic neural networks (New Jersey: Wiley-Interscience)

    Book  Google Scholar 

  • Hou Y, Liao T, Yan J 2007 H ∞ synchronization of chaotic systems using output feedback control design. Physica A 379: 81–89

    Article  MathSciNet  Google Scholar 

  • Hu J, Chen S, Chen L 2005 Adaptive control for anti-synchronization of Chua’s chaotic system. Phys. Lett. A 339: 455–460

    Article  MATH  Google Scholar 

  • Park J H, O K 2005 LMI optimization approach to stabilization of time-delay chaotic systems. Chaos, Solitons and Fractals 23: 445–450

    Article  MATH  MathSciNet  Google Scholar 

  • Ott E, Grebogi C, Yorke J 1990 Controlling chaos. Phys. Rev. Lett. 64: 1196–1199

    Article  MATH  MathSciNet  Google Scholar 

  • Park J 2005 Adaptive synchronization of a unified chaotic systems with an uncertain parameter. Int. J. Nonlinear Sci. Numer. Simul. 6: 201–206

    Google Scholar 

  • Pecora L M, Carroll T L 1996 Synchronization in chaotic systems. Phys. Rev. Lett. 64: 821–824

    Article  MathSciNet  Google Scholar 

  • Stoorvogel A 1992 The H ∞ control problem: A state-space approach (UK: Prentice Hall, International)

    Google Scholar 

  • Wang C, Su J 2004 A new adaptive variable structure control for chaotic synchronization and secure communication. Chaos, Solitons and Fractals 20: 967–977

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Y, Guan Z, Wang H 2003 Feedback an adaptive control for the synchronization of chen system via a single variable. Phys. Lett. A 312: 34–40

    Article  MATH  MathSciNet  Google Scholar 

  • Wu X, Lu J 2003 Parameter identification and backstepping control of uncertain Lü system. Chaos, Solitons and Fractals 18: 721–729

    Article  MATH  MathSciNet  Google Scholar 

  • Yang X, Chen G 2002 Some observer-based criteria for discrete-time generalized chaos synchronization. Chaos, Solitons and Fractals 13: 1303–1308

    Article  MATH  MathSciNet  Google Scholar 

  • Zhan M, Wang X, Gong X, Wei G, Lai C 2003 Complete synchronization and generalized synchronization of one-way coupled time-delay systems. Phys. Rev. E 68: 6208–6213

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Automative Engineering, Seoul National University of Technology, 172 Gongneung 2-dong, Nowon-gu, Seoul, 139-743, India

    Choon Ki Ahn

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  1. Choon Ki Ahn
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Correspondence to Choon Ki Ahn.

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Ahn, C.K. RBF neural network based H ∞ synchronization for unknown chaotic systems. Sadhana 35, 449–460 (2010). https://doi.org/10.1007/s12046-010-0025-x

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  • DOI: https://doi.org/10.1007/s12046-010-0025-x

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