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Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control

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Abstract

This paper investigates the adaptive anti-synchronization problem for time-delayed chaotic neural networks with unknown parameters. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) approach, the adaptive anti-synchronization controller is designed and an analytic expression of the controller with its adaptive laws of unknown parameters is shown. The proposed controller can be obtained by solving the LMI problem. An illustrative example is given to demonstrate the effectiveness of the proposed method.

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References

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

    Article  MathSciNet  ADS  Google Scholar 

  2. Chen, G., Dong, X.: From Chaos to Order. World Scientific, Singapore (1998)

    MATH  Google Scholar 

  3. Zhang, Y., Sun, J.: Chaotic synchronization and anti-synchronization based on suitable separation. Phys. Lett. A 330, 442–447 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. Kim, C.M., Rim, S., Kye, W.H., Ryu, J.W., Park, Y.J.: Anti-synchronization of chaotic oscillators. Phys. Lett. A 320, 39–49 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. Li, C., Liao, X.: Anti-synchronization of a class of coupled chaotic systems via linear feedback control. Int. J. Bifurc. Chaos 16, 1041–1047 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Idowu, B.A., Vincent, U.E., Njah, A.N.: Anti-synchronization of chaos in nonlinear gyros via active control. J. Math. Control Sci. Appl. 1, 191–200 (2007)

    Google Scholar 

  7. Vincent, U.E., Laoye, J.A.: Synchronization, anti-synchronization and current transport in non-identical chaotic ratchets. Physica A 384, 230–240 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  8. Al-sawalha, M.M., Noorania, M.S.M.: On anti-synchronization of chaotic systems via nonlinear control. Chaos Solitons Fractals 42, 170–179 (2009)

    Article  Google Scholar 

  9. Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287–289 (1977)

    Article  ADS  Google Scholar 

  10. Farmer, J.D.: Chaotic attractors of an infinite-dimensional dynamical system. Physica D 4, 366–393 (1982)

    MathSciNet  ADS  Google Scholar 

  11. Lu, H.: Chaotic attractors in delayed neural networks. Phys. Lett. A 298, 109–116 (2002)

    Article  MATH  ADS  Google Scholar 

  12. Park, J.H., Kwon, O.M.: Guaranteed cost control of time-delay chaotic systems. Chaos Solitons Fractals 27, 1011–1018 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen, B., Liu, X., Tong, S.: Guaranteed cost control of time-delay chaotic systems via memoryless state feedback. Chaos Solitons Fractals 34, 1683–1688 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. Guan, X., Feng, G., Chen, C., Chen, G.: A full delayed feedback controller design method for time-delay chaotic systems. Physica D 227, 36–42 (2007)

    MATH  MathSciNet  ADS  Google Scholar 

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

    Article  Google Scholar 

  16. Zhu, W., Xu, D., Huang, Y.: Global impulsive exponential synchronization of time-delayed chaotic systems. Chaos Solitons Fractals 35, 904–912 (2008)

    Article  MATH  Google Scholar 

  17. Liu, X.: Impulsive synchronization of chaotic systems subject to time delay. Nonlinear Anal. Theory Methods Appl. (2009). doi:10.1016/j.na.2009.01.162

    Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  20. Yassen, M.T.: Adaptive synchronization of two different uncertain chaotic systems. Phys. Lett. A 337, 335–341 (2005)

    Article  MATH  ADS  Google Scholar 

  21. Li, S., Xu, W., Li, R.: Synchronization of two different chaotic systems with unknown parameters. Phys. Lett. A 361, 98–102 (2007)

    Article  MATH  ADS  Google Scholar 

  22. Guo, R.: A simple adaptive controller for chaos and hyperchaos synchronization. Phys. Lett. A 372, 5593–5597 (2008)

    Article  ADS  Google Scholar 

  23. Wang, Z.: Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters. Commun. Nonlinear Sci. Numer. Simul. 14, 2366–2372 (2009)

    Article  ADS  Google Scholar 

  24. Al-sawalha, M.M., Noorani, M.S.M.: Anti-synchronization of chaotic systems with uncertain parameters via adaptive control. Phys. Lett. A 373, 2852–2857 (2009)

    Article  ADS  Google Scholar 

  25. Krasovskii, N.N.: Application of Lyapunov’s second method for equations with time delay. Prikl. Mat. Mek. 20, 315–327 (1956)

    MathSciNet  Google Scholar 

  26. Kolmanovskii, V., Nosov, A.: Stability of Functional Differential Equations. Academic Press, San Diego (1986)

    MATH  Google Scholar 

  27. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishinan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)

    Google Scholar 

  28. Noldus, E.: Stabilization of a class of distributional convolutional equations. Int. J. Control 41, 947–960 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  29. Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The Mathworks Inc., Natick (1995)

    Google Scholar 

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Authors and Affiliations

  1. Division of Electronic and Control Engineering, Wonkwang University, Iksan, Korea

    Choon Ki Ahn

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  1. Choon Ki Ahn
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Correspondence to Choon Ki Ahn.

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This paper was supported by Wonkwang University in 2009.

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Ahn, C.K. Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control. Int J Theor Phys 48, 3498 (2009). https://doi.org/10.1007/s10773-009-0154-3

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  • DOI: https://doi.org/10.1007/s10773-009-0154-3

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