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Robust synchronization of uncertain fractional-order chaotic systems with time-varying delay

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Abstract

This paper presents a new technique using a recurrent non-singleton type-2 sequential fuzzy neural network (RNT2SFNN) for synchronization of the fractional-order chaotic systems with time-varying delay and uncertain dynamics. The consequent parameters of the proposed RNT2SFNN are learned based on the Lyapunov–Krasovskii stability analysis. The proposed control method is used to synchronize two non-identical and identical fractional-order chaotic systems, with time-varying delay. Also, to demonstrate the performance of the proposed control method, in the other practical applications, the proposed controller is applied to synchronize the master–slave bilateral teleoperation problem with time-varying delay. Simulation results show that the proposed control scenario results in good performance in the presence of external disturbance, unknown functions in the dynamics of the system and also time-varying delay in the control signal and the dynamics of system. Finally, the effectiveness of proposed RNT2SFNN is verified by a nonlinear identification problem and its performance is compared with other well-known neural networks.

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References

  1. Lee, S., Wong, S.: Group-based approach to predictive delay model based on incremental queue accumulations for adaptive traffic control systems. Transp. Res. Part B Methodol. 98, 1–20 (2017)

    Article  Google Scholar 

  2. Banks, H.T., Banks, J.E., Bommarco, R., Laubmeier, A., Myers, N., Rundlöf, M., Tillman, K.: Modeling bumble bee population dynamics with delay differential equations. Ecol. Model. 351, 14–23 (2017)

    Article  Google Scholar 

  3. Balas, M.J., Frost, S.A.: Normal form for linear infinite-dimensional systems in Hilbert space and its role in direct adaptive control of distributed parameter systems. In: AIAA Guidance, Navigation, and Control Conference, p. 1501 (2017)

  4. Zhou, B., Egorov, A.V.: Razumikhin and Krasovskii stability theorems for time-varying time-delay systems. Automatica 71, 281–291 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Medvedeva, I.V., Zhabko, A.P.: Synthesis of razumikhin and Lyapunov–Krasovskii approaches to stability analysis of time-delay systems. Automatica 51, 372–377 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Sanz, R., García, P., Zhong, Q.-C., Albertos, P.: Predictor-based control of a class of time-delay systems and its application to quadrotors. IEEE Trans. Ind. Electron. 64(1), 459–469 (2017)

    Article  Google Scholar 

  7. Hamamci, S.E.: An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers. IEEE Trans. Autom. Control 52(10), 1964–1969 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lazarević, M.P., Spasić, A.M.: Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach. Math. Comput. Model. 49(3), 475–481 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, X.: Some results of linear fractional order time-delay system. Appl. Math. Comput. 197(1), 407–411 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Chen, Y., Moore, K.L.: Analytical stability bound for a class of delayed fractional-order dynamic systems. Nonlinear Dyn. 29(1), 191–200 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Deng, W., Li, C., Lü, J.: Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn. 48(4), 409–416 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gao, Z.: A computing method on stability intervals of time-delay for fractional-order retarded systems with commensurate time-delays. Automatica 50(6), 1611–1616 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu, F., Li, X., Liu, X., Tang, Y.: Parameter identification of fractional-order chaotic system with time delay via multi-selection differential evolution. Syst. Sci. Control Eng. 5(1), 42–48 (2017)

    Article  Google Scholar 

  14. Stamov, G., Stamova, I.: Impulsive fractional-order neural networks with time-varying delays: almost periodic solutions. Neural Comput. Appl. 28(11), 3307–3316 (2017)

    Article  Google Scholar 

  15. Song, X., Song, S., Li, B., Tejado Balsera, I.: Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications. Trans. Inst. Meas. Control 0142331217714523 (2017)

  16. Hu, W., Ding, D., Wang, N.: Nonlinear dynamic analysis of a simplest fractional-order delayed memristive chaotic system. J. Comput. Nonlinear Dyn. 12(4), 041003 (2017)

    Article  Google Scholar 

  17. Rakkiyappan, R., Udhayakumar, K., Velmurugan, G., Cao, J., Alsaedi, A.: Stability and hopf bifurcation analysis of fractional-order complex-valued neural networks with time delays. Adv. Differ. Equ. 2017(1), 225 (2017)

    Article  MathSciNet  Google Scholar 

  18. Fei-Fei, L., Zhe-Zhao, Z.: Synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive neural network control. Acta Phys. Sin. 66(9) (2017). https://doi.org/10.7498/aps.66.090504

  19. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)

  20. Rong, H.-J., Sundararajan, N., Huang, G.-B., Saratchandran, P.: Sequential adaptive fuzzy inference system (SAFIS) for nonlinear system identification and prediction. Fuzzy Sets Syst. 157(9), 1260–1275 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hokayem, P.F., Spong, M.W.: Bilateral teleoperation: an historical survey. Automatica 42(12), 2035–2057 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sadeghi, M.S., Momeni, H., Amirifar, R.: \({H_\infty }\) and \({L_1}\) control of a teleoperation system via LMIs. Appl. Math. Comput. 206(2), 669–677 (2008)

    MathSciNet  MATH  Google Scholar 

  23. Yingwei, L., Sundararajan, N., Saratchandran, P.: A sequential learning scheme for function approximation using minimal radial basis function neural networks. Neural Comput. 9(2), 461–478 (1997)

    Article  MATH  Google Scholar 

  24. Angelov, P.P., Filev, D.P.: An approach to online identification of Takagi–Sugeno fuzzy models. IEEE Trans. Syst. Man Cybern. Part B Cybern. 34(1), 484–498 (2004)

    Article  Google Scholar 

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Authors and Affiliations

  1. Control Engineering Department, Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran

    Ardashir Mohammadzadeh & Sehraneh Ghaemi

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  1. Ardashir Mohammadzadeh
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  2. Sehraneh Ghaemi
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Correspondence to Sehraneh Ghaemi.

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Mohammadzadeh, A., Ghaemi, S. Robust synchronization of uncertain fractional-order chaotic systems with time-varying delay. Nonlinear Dyn 93, 1809–1821 (2018). https://doi.org/10.1007/s11071-018-4290-2

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