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Global Chaos Synchronization of WINDMI and Coullet Chaotic Systems using Adaptive Backstepping Control Design

Sundarapandian Vaidyanathan|Suresh Rasappan
경북대학교 자연과학대학 수학과|2014.06|Kyungpook Mathematical Journal|제54권 제2호|pp. 293-320|DOI http://dx.doi.org/10.5666/KMJ.2014.54.2.293

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참고문헌

키워드

SynchronizationChaosAdaptive Backstepping ControlWINDMI SystemCoullet System
주제분류수학

초록

In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstep- ping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability the- ory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predeter- mined desired value. The adaptive backstepping control method is effective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the flexibility to construct a control law and estimate the parameter values. Numeri- cal simulations are also given to illustrate and validate the synchronization results derived in this paper.

Abstract

In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstep- ping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability the- ory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predeter- mined desired value. The adaptive backstepping control method is effective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the flexibility to construct a control law and estimate the parameter values. Numeri- cal simulations are also given to illustrate and validate the synchronization results derived in this paper.

참고문헌 (50)

  1. H. Fujisaka, "Stability theory of synchronized motion in coupled-oscillator systems", Progress of Theoretical Physics, 63, pp.32~47 (1983)
  2. L. M. Pecora, "Synchronization in chaotic systems", Phys. Rev. Lett., 64 (1990)
  3. L. M. Pecora, "Synchronizing chaotic circuits", IEEE Trans. Circ. Sys., 38, pp.453~456 (1991)
  4. K. T. Alligood, "Chaos: An Introduction to Dynamical Systems" (1997), Springer-Verlag
  5. Edward Ott, "Chaos in Dynamical Systems" (2002), Cambridge University Press
  6. Y. M. Wang, "Generalized synchronization of continuous chaotic systems", Chaos, Solitons and Fractals, 27, pp.97~101 (2006)
  7. Z. M. Ge, "Phase synchronization of coupled chaotic multiple time scales systems", Chaos, Solitons and Fractals, 20, pp.639~647 (2004)
  8. J. Qiang, "Projective synchronization of a new hyper chaotic Lorenz systems", Phys. Lett. A, 370, pp.40~45 (2007)
  9. Y. Jian-Ping, "Generalized projective synchronization for the chaotic Lorenz systems and the chaotic Chen system", Journal of Shanghai University, 10, pp.299~304 (2006)
  10. R. H. Li, "Adaptive generalized projective synchronization in different chaotic systems based on parameter identifiction", Phys. Lett. A, 367, pp.199~206 (2007)
  11. V. Sundarapandian, "Generalized projective synchronization of double-scroll chaotic systems using active feedback control, CCSIT 2012, Part-I", pp.111~118 (2012), Springer Heldelberg
  12. P. Sarasu, "Generalized projective synchronization of three-scroll chaotic systems via. active control, CCSIT 2012, Part-I", pp.124~133 (2012), Springer Heldelberg
  13. V. Sundarapandian, "Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control", International Journal of Automa-tion and Computing, 9, pp.274~279 (2012)
  14. V. Sundarapandian, "Anti-synchronization of four wing chaotic systems via sliding mode control", International Journal of Signal System Control and Engineering Application, 4, pp.18~25 (2011)
  15. K. Murali, "Secure communication using a compound signal using sampled-data feedback", Applied Mathematics and Mechanics, 11, pp.1309~1315 (2003)
  16. T. Yang, "Generalized synchronization of chaos via linear transfor-mations", Internat. J. Bifur. Chaos, 9, pp.215~219 (1999)
  17. K. Murali, "Chaos in Nonlinear Oscillators: Controlling and Synchronization" (1996), World Scientific
  18. S. K. Han, "D-phasing and bursting in coupled neural oscillators", Phys. Rev. Lett., 75, pp.3190~3193 (1995)
  19. B. Blasius, "Complex dynamics and phase synchronization in spatially extended ecological system", Nature, 399, pp.354~359 (1999)
  20. L. Kocarev, "General approach for chaotic synchronization with appli-cations to communications", Phys. Rev. Lett., 74, pp.5028~5030 (1995)
  21. Zuolei Wang, "Chaos synchronization of an energy resource system based on linear control", Nonlinear Analysis: Real world Application,(article in press), ~
  22. Jiang Wang, "Synchronization of ghostburster neurons in external electrical stimulation via H∞ variable universe fuzzy adaptive control", Chaos, Solitons and Fractals, 39, pp.2076~2085 (2009)
  23. F. M. Moukam Kakmeni, "Chaos synchronization in bi-axial magnets modeled by bloch equation", Chaos, Solitons and Fractals, 30, pp.690~699 (2006)
  24. J. L. Hindmarsh, "A model of neuronal bursting using 3-coupled 1 st order differential equations", Proc. Roy. Soc. Lond. B. Biol, 221, pp.81~102 (1984)
  25. Yan-Qiu Che, "Kai-Ming Tsang and Wai-Lok Chen, Unidirectional syn-chronization for Hindmarsh-Rose neurons via robust adaptive sliding mode control", Nonlinear Analysis: Real world Application, 11, pp.1096~1104 (2010)
  26. Guang Zhao Zeng, "Complexity of an SIR epidemic dynamics model with impulsive vaccination control", Chaos, Solitons and Fractals, 26, pp.495~505 (2005)
  27. Junxa Wang, "Global synchronization for time delay WINDMI system", Chaos, Solitons and Fractals, 30, pp.629~635 (2006)
  28. W. Horton, "Chaos and the limits of predictability for the solar-wind-driven magnetosphere-ionosphere system", Physics of Plasmas, 8, pp.2946~2952 (2003)
  29. W. Horton, "A low-dimentional dynamical model for the solar wind driven geotail-ionosphere system", Journal of Geophysical Research A, 103, pp.4561~4512 (1998)
  30. J. P. Smith, "Dynamical range of WINDMI model: an exploration of possible magnetospheric plasma states", Journal of Geophysical Research A, 105, pp.12983~12996 (2000)
  31. E. Ott, "Controlling chaos", Phys. Rev. Lett., 64, pp.1196~1199 (1990)
  32. J. H. Park, "A novel criterion for delayed feedback control of time-delay chaotic systems", Chaos, Solitons and Fractals, 17, pp.709~716 (2003)
  33. H. T. Yau, "Design of adaptive sliding mode controller for chaos synchronization with uncertainties", Chaos, Solitons and Fractals, 22, pp.341~347 (2004)
  34. V. Sundarapandian, "Global chaos synchronization of the Pehlivan systems by sliding mode control", International J. Computer Science and Engineering, 03, pp.2163~2169 (2011)
  35. V. Sundarapandian, "Global chaos synchronization for Rossler and Ar-neodo chaotic systems by nonlinear control", Far East Journal of Applied Mathematics, 44, pp.137~148 (2010)
  36. V. Sundarapandian, "PEIE 2010", pp.20~27 (2010), Springer-Verlag
  37. X. Wu, "identification and backstepping control of uncertain Lu system", Chaos, Solitons and Fractals, 18, pp.721~729 (2003)
  38. Y. G. Yu, "Adaptive backstepping synchronization of uncertain chaotic systems", Chaos, Solitons and Fractals, 27, pp.1369~1375 (2006)
  39. R. Suresh, "Global chaos synchronization of WINDMI and Coullet chaotic systems using backstepping control", Far East Journal of Mathematical Sciences, 67, pp.265~287 (2012)
  40. R. Suresh, "Hybrid synchronization of n-scroll Chua and Lur'e chaotic systems using backstepping control via novel feedback", Archives of Control Sciences, 22(LVIII), pp.255~278 (2012)
  41. R. Suresh, "Synchronization of n-scroll hyperchaotic Chua circuit using backstepping control with recursive feedback", Far East Journal of Math-ematical Sciences, 73, pp.73~95 (2013)
  42. J. Lu, "Adaptive feedback synchronization of a unified chaotic system", Phys. Lett. A, 329, pp.327~333 (2004)
  43. J. H. Park, "Adaptive synchronization of Genesio-Tesi chaotic system via a novel feedback control", Physics Letters A, 371, pp.263~270 (2007)
  44. J. H. Park, "Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters", J. Computational and Ap-plied Math., 213, pp.288~293
  45. Min Xiao, "Synchronization of a chaotic electronic circuit system with cubic term via adaptive feedback control", Communication in Nonlinear Science and Numerical simulation, 14, pp.3379~3388 (2009)
  46. Yan-Wu Wang, "Adaptive control and synchronization for chaotic systems with parametric uncertainities", Phys. Lett. A., 372, pp.2409~2414 (2008)
  47. Zhiyong Ye, "Adaptive synchronization to a general non-autonomous chaotic system and it applications Nonlinear Analysis", Real World Applications, 13, pp.840~849 (2012)
  48. J. C. Sprott, "Chaos and Time- Series Analysis" (2003), Oxford University Press
  49. P. Coullet, "Transition to stochasticity for a class of forced oscillators", Phys. Lett. A, 72, pp.268~270 (1979)
  50. W. Hahn, "The Stability of Motion" (1967), Springer-Verlag

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