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Robust control for fractional variable-order chaotic systems with non-singular kernel

The European Physical Journal Plus volume 133, Article number: 13 (2018) Cite this article

Abstract.

This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen’s attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.

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References

  1. D. Kumar, R.P. Agarwal, J. Singh, J. Comput. Appl. Math. (2017) https://doi.org/10.1016/j.cam.2017.03.011

  2. K.M. Owolabi, A. Atangana, Adv. Differ. Equ. 2017, 223 (2017)

    Article  Google Scholar 

  3. D. Kumar, J. Singh, D. Baleanu, Rom. Rep. Phys. 69, 103 (2017)

    Google Scholar 

  4. K.M. Owolabi, Commun. Nonlinear Sci. Numer. Simul. 44, 304 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  5. K.M. Owolabi, A. Atangana, Chaos, Solitons Fractals 99, 171 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  6. H. Singh, H.M. Srivastava, D. Kumar, Chaos, Solitons Fractals 103, 131 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  7. K.M. Owolabi, A. Atangana, Eur. Phys. J. Plus 131, 335 (2016)

    Article  Google Scholar 

  8. K.M. Owolabi, Chaos, Solitons Fractals 103, 544 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  9. K.M. Owolabi, Chaos, Solitons Fractals 93, 89 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  10. Y. Khan, M. Fardi, K. Sayevand, M. Ghasemi, Neural Comput. Appl. 24, 187 (2014)

    Article  Google Scholar 

  11. Y. Khan, S.P. Ali Beik, K. Sayevand, A. Shayganmanesh, Quaest. Math. 38, 41 (2015)

    Article  MathSciNet  Google Scholar 

  12. J. Singh, D. Kumar, R. Swroop, S. Kumar, Neur. Comput. Appl. (2017) https://doi.org/10.1007/s00521-017-2909-8

  13. S. Kumar, A. Kumar, Z.M. Odibat, Math. Methods Appl. Sci. 40, 4134 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  14. A. Atangana, A. Secer, Abstr. Appl. Anal. 2013, 279681 (2013)

    Google Scholar 

  15. A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)

    Article  Google Scholar 

  16. S.G. Samko, Anal. Math. 21, 213 (1995)

    Article  MathSciNet  Google Scholar 

  17. B.S.T. Alkahtani, I. Koca, A. Atangana, J. Nonlinear Sci. Appl. 9, 4867 (2016)

    Article  MathSciNet  Google Scholar 

  18. A. Atangana, J. Comput. Phys. 293, 104 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  19. H. Sun, W. Chen, C. Li, Y. Chen, Physica A 389, 2719 (2010)

    Article  ADS  Google Scholar 

  20. A. Atangana, J.F. Botha, Bound. Value Probl. 2013, 53 (2013)

    Article  Google Scholar 

  21. A. Atangana, R.T. Alqahtani, J. Comput. Theor. Nanosci. 13, 2710 (2016)

    Article  Google Scholar 

  22. A. Atangana, J. Comput. Phys. 293, 104 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  23. K. Rajagopal, S. Vaidyanathan, A. Karthikeyan, P. Duraisamy, Electr. Eng. 99, 721 (2017)

    Article  Google Scholar 

  24. H. Wang, Z.Z. Han, Q.Y. Xie, W. Zhang, Commun. Nonlinear Sci. Numer. Simul. 14, 1410 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  25. C. Yin, S.M. Zhong, W.F. Chen, Commun. Nonlinear Sci. Numer. Simul. 17, 356 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  26. X.Y. Wang, Y.J. He, M.J. Wang, Nonlinear Anal. 71, 6126 (2009)

    Article  MathSciNet  Google Scholar 

  27. A. Mohammadzadeh, S. Ghaemi, Neurocomputing 191, 200 (2016)

    Article  Google Scholar 

  28. C. Li, K. Su, J. Zhang, D. Wei, Optik 124, 5807 (2013)

    Article  ADS  Google Scholar 

  29. M. Roopaei, B.R. Sahraei, T.C. Lin, Commun. Nonlinear Sci. Numer. Simul. 15, 4158 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  30. R. Zhang, S. Yang, Nonlinear Dyn. 69, 983 (2012)

    Article  Google Scholar 

  31. A. Ouannas, A.T. Azar, S. Vaidyanathan, Math. Methods Appl. Sci. 40, 1804 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  32. H. Delavari, Int. J. Dyn. Control 5, 102 (2017)

    Article  MathSciNet  Google Scholar 

  33. Z. Hammouch, T. Mekkaoui, Nonauton. Dyn. Syst. (2014) https://doi.org/10.2478/msds-2014-0001

  34. F. Kaiser, Radio Sci. 17, 17 (1982)

    Article  ADS  Google Scholar 

  35. O. Olusola, E. Vincent, N. Njah, E. Ali, Int. J. Nonlinear Sci. 11, 121 (2011)

    MathSciNet  Google Scholar 

  36. A. Abooee, H.A. Yaghini-Bonabi, M.R. Jahed-Motlagh, Commun. Nonlinear Sci. Numer. Simul. 18, 1235 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  37. P. Muthukumar, P. Balasubramaniam, K. Ratnavelu, Chaos 24, 033105 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  38. A.T. Azar, S. Vaidyanathan (Editors), Advances in Chaos Theory and Intelligent Control, in Studies in Fuzziness and Soft Computing, Vol. 337 (Springer, Switzerland, 2016)

  39. S. Panchev, T. Spassova, N.K. Vitanov, Chaos, Solitons Fractals 33, 1658 (2007)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    C. J. Zuñiga-Aguilar & R. F. Escobar-Jiménez

  2. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

  3. Univ. Grenoble Alpes, F-38000, Grenoble, France

    H. M. Romero-Ugalde

  4. CEA LETI MINATEC Campus, F-38054, Grenoble, France

    H. M. Romero-Ugalde

Authors
  1. C. J. Zuñiga-Aguilar
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  2. J. F. Gómez-Aguilar
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  3. R. F. Escobar-Jiménez
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  4. H. M. Romero-Ugalde
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Corresponding author

Correspondence to J. F. Gómez-Aguilar.

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Zuñiga-Aguilar, C.J., Gómez-Aguilar, J.F., Escobar-Jiménez, R.F. et al. Robust control for fractional variable-order chaotic systems with non-singular kernel. Eur. Phys. J. Plus 133, 13 (2018). https://doi.org/10.1140/epjp/i2018-11853-y

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  • DOI: https://doi.org/10.1140/epjp/i2018-11853-y

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