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

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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.

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REFERENCES

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  3. Park, J.H., Synchronization of Genesio chaotic system via backstepping approach, Chaos Solitons Fractals, 2006, vol. 27, no. 5, pp. 1369–1375.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

  8. Engheta, N., On the role of fractional calculus in electromagnetic theory, IEEE Antennas Propag. Mag., 1997, vol. 39, no. 4, pp. 35–46.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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/10.1177/1687814016656704

  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. 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. 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.

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

  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.

  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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    MATH  Google Scholar 

  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.

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Authors and Affiliations

  1. Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Arash Pourhashemi, Amin Ramezani & Mehdi Siahi

  2. Department of Electrical and Computer Engineering,Tarbiat Modares University, Tehran, Iran

    Amin Ramezani

Authors
  1. Arash Pourhashemi
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  2. Amin Ramezani
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  3. Mehdi Siahi
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Correspondence to Arash Pourhashemi or Amin Ramezani.

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Pourhashemi, A., Ramezani, A. & Siahi, M. Design of New Fractional Sliding Mode Control Due to Complete Synchronization of Commensurate and Incommensurate Fractional Order Chaotic Systems. Aut. Control Comp. Sci. 52, 505–516 (2018). https://doi.org/10.3103/S0146411618060093

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  • DOI: https://doi.org/10.3103/S0146411618060093

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