American Journal of Embedded Systems and Applications

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Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System

Received: Oct. 13, 2018    Accepted: Oct. 31, 2018    Published: Dec. 14, 2018
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Abstract

This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.

DOI 10.11648/j.ajesa.20180602.11
Published in American Journal of Embedded Systems and Applications ( Volume 6, Issue 2, December 2018 )
Page(s) 69-74
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Delay, Fractional-Order, Chaotic System, Impulsive, Synchronization

References
[1] B. Ross, Fractional calculus and its applications, in: Proceedings of the International Conference held at the University of New Haven (Lecture Notes in Mathematics, vol. 457), Springer-Verlag, Berlin, 1975.
[2] R. Hilfer, Applications of fractional calculus in physics, World Scientific, New Jersey, 2001.
[3] K. Diethelm, The analysis of fractional differential equations, Springer-Verlag, Berlin, 2010.
[4] R. L. Magin, Fractional Calculus in Bioengineering, Begell House Publisher, Connecticut, 2006.
[5] G. R. Chen, T. Ueta, Yet another chaotic attractor, International Journal of Bifurcation and Chaos 9 (7) (1999) 1465-1466.
[6] I. Petras, A note on the fractional-order Chua’s system, Chaos Solitons & Fractals 38 (1) (2008) 140-147.
[7] B. Wang, C. Wu, D. L. Zhu, A new double-wing fractional-order chaotic system and its synchronization by sliding mode, Acta Physica Sinica, 62 (23) (2013) 2305061-23050616.
[8] T. T. Hu, X. J. Zhang, S. M. Zhong, Global asymptotic synchronization of nonidentical fractional-order neural networks, Neurocomputing, 313 (2018) 39-46.
[9] Y. S. Chen, C. C. Chang, Impulsive synchronization of Lipschitz chaotic systems, Chaos Solitons & Fractals 40 (3) (2009) 1221-1228.
[10] M. Haeri, M. Dehghani, Robust stability of impulsive synchronization in hyper-chaotic systems, Communications in Nonlinear Science & Numerical Simulation 14 (3) (2009) 880-891.
[11] D. Ghosh, A. R. Chowdhury, Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors, Nonlinear Dynamics 60 (2010) 607-613.
[12] T. Yang, Impulsive control, IEEE Transactions on Automatic Control 44 (5) (1999) 1081-1083.
[13] T. Yang, Impulsive Control Theory, Springer-Verlag, Berlin, 2001.
[14] T. Yang, Impulsive Systems and Control: Theory and Application, Nova Science Publishers, Huntington, 2001.
[15] T. D. Ma, W. B. Jiang, J. Fu, Impulsive synchronization of fractional order hyperchaotic systems based on comparison system, Acta Physica Sinica 61 (9) (2012) 0905031-0905036.
[16] J. G. Liu, A novel study for impulsive synchronization of fractional-order chaotic systems, Chinese Physics B 22 (2013) 0605101-0605104.
[17] L. P. Zhang, H. B. Jiang, Q. S. Bi, Adaptive impulsive synchronization for a class of non-autonomous chaotic systems, Journal of Dynamics and Control 6 (2008) 312–315. (In Chinese)
[18] C. L. Li, Y. N. Tong, H. M. Li, K. L. Su, Adaptive impulsive synchronization of a class of chaotic and hyperchaotic systems, Physica Scripta 86 (5) (2012) 055003.
[19] H. L. Xi, S. M. Yu, R. X. Zhang, L. Xu, Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems, Optik 125 (9) (2014) 2036-2040.
[20] J. K. Hale, S. M. Verdugn Lunel, Introduction to functional differential equations, Springer-Verlag, New York, 1991.
[21] W. H. Deng, Y. J. Wu, C. P. Li, Stability analysis of differential equations with time-dependent delay, International Journal of Bifurcation and Chaos 16 (2) (2006) 465-472.
[22] C. P. Li, W. G. Sun, J. Kurths, Synchronization of complex dynamical networks with time delays, Physica A 361 (1) (2006) 24-34.
[23] C. P. Li, W. Q. Sun, D. L. Xu, Synchronization of complex dynamical networks with nonlinear inner-coupling functions and time delays, Progress of Theoretical Physics 114 (4) (2005) 749-761.
[24] W. H. Deng, C. P. Li, J. H. Lü, Stability analysis of linear fractional differential system with multiple time delays, Nonlinear Dynamics 48 (2007) 409-416.
[25] Y. J. Gu, Y. G. Yu, H. Wang, Synchronization for fractional-order time-delayed memristor- based neural networks with parameter uncertainty, Journal of the Franklin Institute 353 (15) (2016) 3657-3684.
[26] L. Z. Zhang, Y. Q. Yang, F. Wang, X. Sui, Lag synchronization for fractional-order memristive neural networks with time delay via switching jumps mismatch, Journal of the Franklin Institute 355 (3) (2018) 1217-1240.
[27] R. D. Zhang, Q. Zou, Z. X. Cao, F. R. Gao, Design of fractional order modeling based extended non-minimal state space MPC for temperature in an industrial electric heating furnace, Journal of Process Control 56 (2017) 13-22.
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  • APA Style

    Changyou Wang, Yuan Zhuo, Xingcheng Pu, Yonghong Li, Rui Li. (2018). Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. American Journal of Embedded Systems and Applications, 6(2), 69-74. https://doi.org/10.11648/j.ajesa.20180602.11

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    ACS Style

    Changyou Wang; Yuan Zhuo; Xingcheng Pu; Yonghong Li; Rui Li. Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. Am. J. Embed. Syst. Appl. 2018, 6(2), 69-74. doi: 10.11648/j.ajesa.20180602.11

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    AMA Style

    Changyou Wang, Yuan Zhuo, Xingcheng Pu, Yonghong Li, Rui Li. Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System. Am J Embed Syst Appl. 2018;6(2):69-74. doi: 10.11648/j.ajesa.20180602.11

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  • @article{10.11648/j.ajesa.20180602.11,
      author = {Changyou Wang and Yuan Zhuo and Xingcheng Pu and Yonghong Li and Rui Li},
      title = {Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System},
      journal = {American Journal of Embedded Systems and Applications},
      volume = {6},
      number = {2},
      pages = {69-74},
      doi = {10.11648/j.ajesa.20180602.11},
      url = {https://doi.org/10.11648/j.ajesa.20180602.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajesa.20180602.11},
      abstract = {This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Adaptive Impulsive Synchronization for a Class of Delay Fractional-Order Chaotic System
    AU  - Changyou Wang
    AU  - Yuan Zhuo
    AU  - Xingcheng Pu
    AU  - Yonghong Li
    AU  - Rui Li
    Y1  - 2018/12/14
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ajesa.20180602.11
    DO  - 10.11648/j.ajesa.20180602.11
    T2  - American Journal of Embedded Systems and Applications
    JF  - American Journal of Embedded Systems and Applications
    JO  - American Journal of Embedded Systems and Applications
    SP  - 69
    EP  - 74
    PB  - Science Publishing Group
    SN  - 2376-6085
    UR  - https://doi.org/10.11648/j.ajesa.20180602.11
    AB  - This paper is concerned with the adaptive impulsive synchronization for a class of delay fractional-order chaotic system. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, based on the Lyapunov stability theory and the generalized Barbalat’s lemma, some new sufficient conditions are derived to guarantee the asymptotic stability of synchronization error system.
    VL  - 6
    IS  - 2
    ER  - 

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Author Information
  • College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China; College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, P. R. China; College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

  • College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

  • College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

  • College of Science, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

  • College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, P. R. China

  • Section