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Volume 6 Issue 1
Jan.  2019

IEEE/CAA Journal of Automatica Sinica

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Hadi Delavari and Milad Mohadeszadeh, "Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 228-235, Jan. 2019. doi: 10.1109/JAS.2016.7510145
Citation: Hadi Delavari and Milad Mohadeszadeh, "Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 228-235, Jan. 2019. doi: 10.1109/JAS.2016.7510145

Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication

doi: 10.1109/JAS.2016.7510145
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  • This paper proposes a novel adaptive sliding mode control (SMC) method for synchronization of non-identical fractional-order (FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances, finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller (ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization (PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.

     

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  • [1]
    I. Podlubny, Fractional Differential Equations. New York, USA:Academic Press, 1999.
    [2]
    V. V. Uchaikin, "Fractional derivatives for physicists and engineers, " Nonlinear Physical Science. Berlin, Germany:Springer, 2013.
    [3]
    D. Baleanu, J. A. T. Machado, and A. C. J. Luo, Fractional Dynamics and Control. New York:Springer, 2012.
    [4]
    R. Hilfer, Applications of Fractional Calculus in Physics. Singapore:World Scientific, 2000.
    [5]
    K. P. Wilkie, C. S. Drapaca, and S. Sivaloganathan, "A nonlinear viscoelastic fractional derivative model of infant hydrocephalus, " Applied Mathematics and Computation, vol. 217, no. 21, pp. 8693-8704, 2011. doi: 10.1016/j.amc.2011.03.115
    [6]
    A. M. Tusset, J. M. Balthazar, D. G. Bassinello, B. R. Jr Pontes, and J. L. Palacios Felix, "Statements on chaos control designs, including a fractional order dynamical system, applied to a "MEMS" comb-drive actuator", Nonlinear Dynamics, vol. 69, no. 4, pp. 1837-1857, 2012. doi: 10.1007/s11071-012-0390-6
    [7]
    Q. G. Yang and C. B. Zeng, "Chaos in fractional conjugate Lorenz system and its scaling attractors, " Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 4041-4051, 2010. doi: 10.1016/j.cnsns.2010.02.005
    [8]
    J. G. Lu and G. R. Chen, "A note on the fractional-order Chen system, " Chaos, Solitons & Fractals, vol. 27, no. 3, pp. 685-688, 2006. http://www.sciencedirect.com/science/article/pii/S0960077905003590
    [9]
    H. Delavari, D. M. Senejohnny, and D. Baleanu, "Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter, " Central European J. Physics, vol. 10, no. 5, pp. 1095-1101, 2012. doi: 10.2478/s11534-012-0073-4
    [10]
    L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems, " Physical Review Letters, vol. 64, no. 8, pp. 821-824, 1990. doi: 10.1103/PhysRevLett.64.821
    [11]
    M. PAghababa and H. PAghababa, "A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs, " Nonlinear Dynamics, vol. 69, no. 4, pp. 1903-1914, 2012. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=a4abaf494759692ac715e58d69ac9d78
    [12]
    M. R. Faieghi, H. Delavari, and D. Baleanu, "A note on stability of sliding mode dynamics in suppression of fractional-order chaotic systems, " Computers and Mathematics with Applications, vol. 66, no. 5, pp. 832-837, 2013. doi: 10.1016/j.camwa.2012.11.015
    [13]
    L. F. Zhang, X. L. An, and J. G. Zhang, "A new chaos synchronization scheme and its application to secure communications, " Nonlinear Dynamics, vol. 73, no. 1-2, pp. 705-722, 2013. doi: 10.1007/s11071-013-0824-9
    [14]
    T. Dasgupta, P. Paralt, and S. Bhattacharya, "Fractional order sliding mode control based chaos synchronization and secure communication, " in Proc. 2015 Int. Conf. Computer Communication and Informatics, Coimbatore, India: IEEE, 2015, 1-6. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7218161
    [15]
    M. Sheikhan, R. Shahnazi, and S. Garoucy, "Synchronization of general chaotic systems using neural controllers with application to secure communication, " Neural Computing and Applications, vol. 22, no. 2, pp. 361-373, 2013. doi: 10.1007/s00521-011-0697-0
    [16]
    M. R. Faieghi, H. Delavari, and D. Baleanu, "A note on stability of sliding mode dynamics in suppression of fractional-order chaotic systems, " Computers and Mathematics with Applications, vol. 66, no. 5, pp. 832-837, 2013. doi: 10.1016/j.camwa.2012.11.015
    [17]
    X. J. Wu, H. Wang, and H. T. Lu, "Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication, " Nonlinear Analysis:Real World Applications, vol. 13, no.3, pp. 1441-1450, 2012. doi: 10.1016/j.nonrwa.2011.11.008
    [18]
    T. Ma, D. Guo, and Q. Xi, "Adaptive synchronization for a class of uncertain fractional order chaotic systems with random perturbations: theory and experiment, " in Proc. 27th Chinese Control and Decision Conf., Qingdao, China: IEEE, 2015, 1309-1314.
    [19]
    M. Mohadeszadeh and H. Delavari, "Synchronization of fractional-order hyper-chaotic systems based on a new adaptive sliding mode control, " Int. J. Dynamics and Control, doi: 10.1007/s40435-015-0177-y, 2015.
    [20]
    M. R. Faieghi, H. Delavari, and D. Baleanu, "Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control, " J. Vibration and Control, vol. 18, no. 9, pp. 1366-1374, 2012. doi: 10.1177/1077546311422243
    [21]
    Z. Gao and X. Z. Liao, "Active disturbance rejection control for synchronization of different fractional-order chaotic systems, " in Proc. 11th World Congress on Intelligent Control and Automation (WCICA). Shenyang, China: IEEE, 2014, 2699-2704.
    [22]
    F. Zhang, G. Chen, C. Li, and J. Kurth, "Chaos synchronization in fractional differential systems, " Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 371, no. 1990, pp. 20120155, 2013.
    [23]
    M. P. Aghababa, "Robust finite-time stabilization of fractional-order chaotic systems based on fractional Lyapunov stability theory, " J. Computational and Nonlinear Dynamics, vol. 7, no. 2, pp. 021010, 2012. doi: 10.1115/1.4005323
    [24]
    M. S. Tavazoei and M. Haeri, "Synchronization of chaotic fractionalorder systems via active sliding mode controller, " Physica A, vol. 387, no. 1, pp. 57-70, 2008. doi: 10.1016/j.physa.2007.08.039
    [25]
    A. E. Matouk and A. A. Elsadany, "Achieving synchronization between the fractional-order hyperchaotic Novel and Chen systems via a new nonlinear control technique, " Applied Mathematics Letters, vol. 29, no. 1, pp. 30-35, 2014. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=47f2d6ed4d5258558ddbb24ad653c1fb
    [26]
    U. E. Vincent and R. Guo, "Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller, " Physics Letters A, vol. 375, no. 24, pp. 2322-2326, 2011. doi: 10.1016/j.physleta.2011.04.041
    [27]
    H. L. Xi, S. M. Yu, R. X. Xu, and L. Zhang, "Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems, " Optik-Int. J. for Light and Electron Optics, vol. 125, no. 9, pp. 2036-2040, 2014. doi: 10.1016/j.ijleo.2013.12.002
    [28]
    J. J. Yan, M. L. Hung, T. Y. Chiang, and Y. S. Yang, "Robust synchronization of chaotic systems via adaptive sliding mode control, " Physics Letters A, vol. 356, no. 3, pp. 220-225, 2006. doi: 10.1016/j.physleta.2006.03.047
    [29]
    M. Mohadeszadeh and H. Delavari, "Synchronization of uncertain fractional-order hyper-chaotic systems via a novel adaptive interval type-2 fuzzy active sliding mode controller, " Int. J. Dynamics and Control, doi: 10.1007/s40435-015-0207-9, 2015.
    [30]
    S. Das, M. Srivastava, and A. Y. T. Leung, "Hybrid phase synchronization between identical and nonidentical three-dimensional chaotic systems using the active control method, " Nonlinear Dynamics, vol. 73, no. 4, pp. 2261-2272, 2013. doi: 10.1007/s11071-013-0939-z
    [31]
    R. Z. Luo, Y. L. Wang, and S. C. Deng, "Combination synchronization of three classic chaotic systems using active backstepping design, " Chaos, vol. 21, pp. 043114, 2011. doi: 10.1063/1.3655366
    [32]
    M. L. Hung, J. S. Lin, J. J. Yan, and T. L. Liao, "Optimal PID control design for synchronization of delayed discrete chaotic systems, " Chaos, Solitons & Fractals, vol. 35, no. 4, pp. 781-785, 2008. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=d416ae5736b1cf1b23e35e1bb4ac71dc
    [33]
    R. Behinfaraz and M. A. Badamchizadeh, "Synchronization of different fractional-ordered chaotic systems using optimized active control, " in Proc. 6th Int. Conf. Modeling Simulation and Applied Optimization (ICMSAO), Istanbul, Turkey: IEEE, 2015, 1-6.
    [34]
    M. R. Faieghi, S. Kuntanapreeda, H. Delavari, and D. Baleanu, "Robust stabilization of fractional-order chaotic systems with linear controllers:LMI-based sufficient conditions, " J. Vibration and Control, vol. 20, no. 7, pp. 1042-1051, 2014. doi: 10.1177/1077546312475151
    [35]
    D. M. Senejohnny and H. Delavari, "Active sliding observer scheme based fractional chaos synchronization, " Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4373-4383, 2012. doi: 10.1016/j.cnsns.2012.03.004
    [36]
    I. N'Doye, H. Voos, and M. Darouach, "Observer-based approach for fractional-order chaotic synchronization and secure communication, " IEEE J. Emerging and Selected Topics in Circuits and Systems, vol. 3, no. 3, pp. 442-450, 2013. doi: 10.1109/JETCAS.2013.2265792
    [37]
    K. Diethelm, N. J. Ford, and A. D. Freed, "A predictor-corrector approach for the numerical solution of fractional differential equations, " Nonlinear Dynamics, vol. 29, no. 1-4, pp. 3-22, 2002. doi: 10.1023/A:1016592219341
    [38]
    K. Diethelm, N J Ford, and A D Freed, "Detailed error analysis for a fractional Adams method, " Numerical Algorithms, vol. 36, no. 1, pp. 31-52, 2004. doi: 10.1023/B:NUMA.0000027736.85078.be
    [39]
    C. P. Li and W. H. Deng, "Remarks on fractional derivatives, " Applied Mathematics and Computation, vol. 187, no. 2, pp. 777-784, 2007. doi: 10.1016/j.amc.2006.08.163
    [40]
    V. I. Utkin, Sliding Modes in Control and Optimization. Heidelberg, Germany:Springer-Verlag, 1992, pp. 66-73.
    [41]
    A. Pisano, M. R. Rapaić, Z. Jeličić, and E. Usai, "Sliding mode control approaches to the robust regulation of linear multivariable fractionalorder dynamics, " Int. J. Robust and Nonlinear Control, vol. 20, no. 18, pp. 2045-2056, 2010. doi: 10.1002/rnc.v20.18
    [42]
    J. J. E. Slotine and W. P. Li, Applied Nonlinear Control. USA:Prentice Hall, 1991.
    [43]
    J. Kennedy and R. Eberhart, "Particle swarm optimization, " in Proc. 4th IEEE Int. Conf. Neural Networks, Perth, WA: IEEE, 1995, 1942-1948.
    [44]
    R. Eberhart and J. Kennedy, "A new optimizer using particle swarm theory, " in Proc. 6th Int. Symposium on Micro Machine and Human Science, Nagoya: IEEE, 1995, 39-43.
    [45]
    H. Q. Li, X. F. Liao, and M. W. Luo, "A novel non-equilibrium fractional-order chaotic system and its complete synchronization by circuit implementation, " Nonlinear Dynamics, vol. 68, no. 1-2, pp. 137-149, 2012. doi: 10.1007/s11071-011-0210-4
    [46]
    D. Zhu, L. Liu, C. Liu, X. Pang, and B. Yan, "Adaptive projective synchronization of a novel fractional-order hyperchaotic system, " in Proc. 9th IEEE Conf. Industrial Electronics and Applications, Hangzhou, China: IEEE, 2014, 814-818.

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