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Automatic Control and Computer Sciences

, Volume 52, Issue 6, pp 505–516 | Cite as

Design of New Fractional Sliding Mode Control Due to Complete Synchronization of Commensurate and Incommensurate Fractional Order Chaotic Systems

  • Arash PourhashemiEmail author
  • Amin RamezaniEmail author
  • Mehdi Siahi
Article
  • 11 Downloads

Abstract

Synchronization between two nonlinear chaotic systems is an interesting problem in both theoretical as well as practical point of view. In this manuscript, the goal is introducing a fractional sliding surface and then design of a fractional sliding mode controller so as to synchronize two fractional nonlinear chaotic systems. The proposed method is performed to synchronize a class of fractional-order chaotic systems in the presence of uncertainties and external disturbances. Stability of the controlled system investigated and analysed by Lyapunov stability theory. The method applied on different example and numerical simulations are performed to show the applicability of the proposal. It is worth mentioning that the novel fractional sliding mode controller can be applied in order to control a broad range of fractional order dynamic systems.

Keywords:

chaotic system fractional-order sliding surface stabilization synchronization Lyapunov stability 

REFERENCES

  1. 1.
    Jayaram, A. and Tadi, M., Synchronization of chaotic systems based on SDRE method, Chaos Solitons Fractals, 2006, vol. 28, no. 3, pp. 707–715.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bhalekar, S. and Daftardar-Gejji, V., Synchronization of different fractional order chaotic systems using active control, Commun. Nonlinear Sci. Numer. Simul., 2010, vol. 15, no. 11, pp. 3536–3546.CrossRefzbMATHGoogle Scholar
  3. 3.
    Park, J.H., Synchronization of Genesio chaotic system via backstepping approach, Chaos Solitons Fractals, 2006, vol. 27, no. 5, pp. 1369–1375.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hosseinnia, S.H., Ghaderi, R., Ranjbar, N.A., Mahmoudian, M., and Momani, S., Sliding mode synchronization of an uncertain fractional order chaotic system, Comput. Math. Appl., 2010, vol. 59, no. 5, pp. 1637–1643.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hosseinnia, S.H., Ghaderi, R., Ranjbar, N.A., Mahmoudian, M., and Momani, S., Sliding mode synchronization of an uncertain fractional order chaotic system, Comput. Math. Appl., 2010, vol. 59, no. 5, pp. 1637–1643.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Wang, W. and Fan, Y., Synchronization of Arneodo chaotic system via backstepping fuzzy adaptive control, Optik (Stuttgart), 2015, vol. 126, no. 20, pp. 2679–2683.CrossRefGoogle Scholar
  7. 7.
    Pisano, A., Rapaić, M., Jeličić, Z., and Usai, E., Nonlinear fractional PI control of a class of fractional-order systems, IFAC Proc. Vol., 2012, vol. 45, no. 3, pp. 637–642.Google Scholar
  8. 8.
    Engheta, N., On the role of fractional calculus in electromagnetic theory, IEEE Antennas Propag. Mag., 1997, vol. 39, no. 4, pp. 35–46.CrossRefGoogle Scholar
  9. 9.
    Yang, X.J., Liao, M.K., and Chen, J.W., A novel approach to processing fractal signals using the Yang-Fourier transforms, Procedia Eng., 2012, vol. 29, pp. 2950–2954.CrossRefGoogle Scholar
  10. 10.
    Guyomar, D., Ducharne, B., Sebald, G., and Audiger, D., Fractional derivative operators for modeling the dynamic polarization behavior as a function of frequency and electric field amplitude, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2009, vol. 56, no. 3, pp. 437–443.CrossRefGoogle Scholar
  11. 11.
    Arshad, S., Baleanu, D., Huang, J., Tang, Y., and Al Qurashi, M.M., Dynamical analysis of fractional order model of immunogenic tumors, Adv. Mech. Eng., 2016, vol. 8, no. 7. https://doi.org/10.1177/1687814016656704Google Scholar
  12. 12.
    N’Doye, I., Voos, H., and Darouach, M., Chaos in a fractional-order cancer system, Eur. Control Conf. ECC 2014, 2014, pp. 171–176.Google Scholar
  13. 13.
    Deng, W.H. and Li, C.P., Chaos synchronization of the fractional Lü system, Phys. A Stat. Mech. Its Appl., 2005, vol. 353, nos. 1–4, pp. 61–72.Google Scholar
  14. 14.
    Jiang, W., Synchronization of a class of fractional-order chaotic systems via adaptive sliding mode control, Proceedings of 2013 IEEE International Conference on Vehicular Electronics and Safety, 2013, pp. 229–233.Google Scholar
  15. 15.
    Khanzadeh, A. and Pourgholi, M., Robust synchronization of fractional-order chaotic systems at a pre-specified time using sliding mode controller with time-varying switching surfaces, Chaos Solitons Fractals, 2016, vol. 91, pp. 69–77.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Zhao, L. and Jia, Y., Neural network-based distributed adaptive attitude synchronization control of spacecraft formation under modified fast terminal sliding mode, Neurocomputing, 2016, vol. 171, pp. 230–241.CrossRefGoogle Scholar
  17. 17.
    Jing, T., Chen, F., and Zhang, X., Finite-time lag synchronization of time-varying delayed complex networks via periodically intermittent control and sliding mode control, Neurocomputing, 2016, vol. 199, pp. 178–184.CrossRefGoogle Scholar
  18. 18.
    Lei, J., Sliding mode synchronization of second order chaotic subsystem based on equivalent transfer function method, Optik, 2016, vol. 127, no. 20, pp. 9056–9072.CrossRefGoogle Scholar
  19. 19.
    Xu, Y. and Wang, H., Synchronization of fractional-order chaotic systems with Gaussian fluctuation by sliding mode control, Abstr. Appl. Anal., 2013, vol. 2013.Google Scholar
  20. 20.
    Xiaomei Yan, R.J., Ting Shang, and Xiaoguo Zhao, Synchronization of a novel class of fractional-order uncertain chaotic systems via adaptive sliding mode controller, Int. J. Control Autom., 2016, vol. 9, no. 1, pp. 1444–1449.Google Scholar
  21. 21.
    Chen, D., Zhang, R., Clinton Sprott, J., and Ma, X., Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control, Nonlinear Dyn., 2012, vol. 70, no. 2, pp. 1549–1561.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Soukkou, A., Boukabou, A., and Leulmi, S., Design and optimization of generalized prediction-based control scheme to stabilize and synchronize fractional-order hyperchaotic systems, Optik (Stuttgart), 2016, vol. 127, no. 12, pp. 5070–5077.CrossRefzbMATHGoogle Scholar
  23. 23.
    Almatroud Othman, A., Noorani, M.S.M., and Al-Sawalha, M.M., Adaptive dual synchronization of chaotic and hyperchaotic systems with fully uncertain parameters, Optik (Stuttgart), 2016, vol. 127, no. 19, pp. 7852–7864.CrossRefzbMATHGoogle Scholar
  24. 24.
    Varan, M., Yalçın, F., and Uyaroğlu, Y., Synchronizations and secure communication applications of a third degree Malasoma system with chaotic flow, Optik (Stuttgart), 2016, vol. 127, no. 23.Google Scholar
  25. 25.
    Dasgupta, T., Paral, P., and Bhattacharya, S., Fractional order sliding mode control based chaos synchronization and secure communication, 2015 International Conference on Computer Communication and Informatics (ICCCI), Coimbatore, 2015, pp. 1–6.Google Scholar
  26. 26.
    Aghababa, M.P., Design of hierarchical terminal sliding mode control scheme for fractional-order systems, IET Sci. Meas. Technol., 2015, vol. 9, no. 1, pp. 122–133.CrossRefGoogle Scholar
  27. 27.
    Hosseinnia, S.H., Ghaderi, R., Ranjbar, N.A., Mahmoudian, M., and Momani, S., Sliding mode synchronization of an uncertain fractional order chaotic system, Comput. Math. Appl., 2010, vol. 59, no. 5, pp. 1637–1643.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Aghababa, M.P., Design of hierarchical terminal sliding mode control scheme for fractional-order systems, IET Sci. Meas. Technol., 2015, vol. 9, no. 1, pp. 122–133.CrossRefGoogle Scholar
  29. 29.
    Moghadam, A.M. and Balochian, S., Synchronization of economic systems with fractional order dynamics using active sliding mode control, Asian Econ. Fin. Rev., 2014, vol. 4, no. 5, pp. 692–704.Google Scholar
  30. 30.
    Vafaei, V., Kheiri, H., and Javidi, M., Chaotic dynamics and synchronization of fractional order PMSM system, Sahand Commun. Math. Anal., 2015, vol. 2, no. 2, pp. 83–90.zbMATHGoogle Scholar
  31. 31.
    Zhang, Y., Zhang, X., and Zhang, Y., Dynamical behavior analysis and control of a fractional-order discretized tumor model, 2016 International Conference on Information Engineering and Communications Technology (IECT 2016), 2016.Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Central Tehran Branch, Islamic Azad UniversityTehranIran
  2. 2.Department of Electrical and Computer Engineering,Tarbiat Modares UniversityTehranIran

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