Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication

Hongtao Liang; Zhen Wang; Zongmin Yue; Ronghui Lu

Kybernetika (2012)

  • Volume: 48, Issue: 2, page 190-205
  • ISSN: 0023-5954

Abstract

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A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are showed by using numerical and experimental simulations.

How to cite

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Liang, Hongtao, et al. "Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication." Kybernetika 48.2 (2012): 190-205. <http://eudml.org/doc/246442>.

@article{Liang2012,
abstract = {A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are showed by using numerical and experimental simulations.},
author = {Liang, Hongtao, Wang, Zhen, Yue, Zongmin, Lu, Ronghui},
journal = {Kybernetika},
keywords = {fractional chaotic systems; fractional differential controller; GS; state observer; Gershgorin circle theorem; pole assignment algorithm; SC; chaotic masking; fractional chaotic systems; fractional differential controller; generalized synchronization; state observer; Gershgorin circle theorem; pole assignment algorithm; secure communication; chaotic masking},
language = {eng},
number = {2},
pages = {190-205},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication},
url = {http://eudml.org/doc/246442},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Liang, Hongtao
AU - Wang, Zhen
AU - Yue, Zongmin
AU - Lu, Ronghui
TI - Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 2
SP - 190
EP - 205
AB - A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are showed by using numerical and experimental simulations.
LA - eng
KW - fractional chaotic systems; fractional differential controller; GS; state observer; Gershgorin circle theorem; pole assignment algorithm; SC; chaotic masking; fractional chaotic systems; fractional differential controller; generalized synchronization; state observer; Gershgorin circle theorem; pole assignment algorithm; secure communication; chaotic masking
UR - http://eudml.org/doc/246442
ER -

References

top
  1. M. A. Aon, S. Cortassa, D. Lloyd, 10.1006/cbir.2000.0572, Cell Biology Internat. 24 (2000), 581-587. DOI10.1006/cbir.2000.0572
  2. K. B. Arman, K. Fallahi, N. Pariz, H. Leung, 10.1016/j.cnsns.2007.11.011, Comm. Nonlinear Sci. Numer. Simul. 14 (2009), 863-879. Zbl1221.94049MR2449755DOI10.1016/j.cnsns.2007.11.011
  3. S. Banerjee, D. Ghosh, A. C. Roy, 10.1088/0031-8949/78/01/015010, Physica Scripta 78 (2008), 015010. Zbl1166.34041MR2447532DOI10.1088/0031-8949/78/01/015010
  4. A. Charef, H. H. Sun, Y. Y. Tsao, B. Onaral, Fractal system as represented by singularity function., IEEE Trans. Automat. Control 37 (1992),1465-1470. Zbl0825.58027MR1183117
  5. M. J. Chen, D. P. Li, A. J. Zhang, 10.1007/BF02918650, J. Marine Sci. Appl. 3 (2004), 64-70. DOI10.1007/BF02918650
  6. G. Chen, X. Yu, Chaos Control: Theory and Applications., Springer, Berlin 2003. Zbl1029.00015MR2014603
  7. K. Diethelm, N. J. Ford, A. D. Freed, 10.1023/A:1016592219341, Nonlinear Dynamics 29 (2002), 3-22. Zbl1009.65049MR1926466DOI10.1023/A:1016592219341
  8. K. Diethelm, N. J. Ford, A. D. Freed, 10.1023/B:NUMA.0000027736.85078.be, Numerical Algorithms 36 (2004), 31-52. Zbl1055.65098MR2063572DOI10.1023/B:NUMA.0000027736.85078.be
  9. D. Ghosh, 10.1007/s11071-009-9538-4, Nonlinear Dynamics 59 (2010), 179-190. Zbl1183.70050MR2585292DOI10.1007/s11071-009-9538-4
  10. R. M. Guerra, W. Yu, 10.1142/S0218127408020264, Internat. J. Bifurcation Chaos 18 (2008), 235-243. Zbl1146.93317MR2400832DOI10.1142/S0218127408020264
  11. J. B. Hu, Y. Han, L. D. Zhao, Synchronizing fractional chaotic systems based on Lyapunov equation., Acta Physica Sinica 57 (2008), 7522-7526. Zbl1199.37060MR2516989
  12. J. B. Hu, Y. Han, L. D. Zhao, 10.1088/1742-6596/96/1/012151, J. Physics: Conference Series 96 (2008), 012151. DOI10.1088/1742-6596/96/1/012151
  13. A. A. Koronovskii, O. I. Moskalenko, A. E. Hramov, 10.3367/UFNe.0179.200912c.1281, Physics-Uspekhi 52 (2009), 1213-1238. DOI10.3367/UFNe.0179.200912c.1281
  14. J. H. Lü, G. R. Chen, 10.1142/S0218127406015179, Internat. J. Bifurcation Chaos 16 (2006), 775-858. DOI10.1142/S0218127406015179
  15. J. H. Lü, G. R. Chen, X. H. Yu, H. Leung, Design and analysis of multiscroll chaotic attractors from saturated function series., IEEE Trans. Circuits Systems - I: Regular Papers 51 (2003), 2476-2490. MR2104664
  16. J. H. Lü, G. R. Chen, S. C. Zhang, 10.1016/S0960-0779(02)00007-3, Chaos, Solitons Fractals 14 (2002), 669-672. Zbl1067.37042MR1906649DOI10.1016/S0960-0779(02)00007-3
  17. J. H. Lü, F. L. Han, X. H. Yu, G. R. Chen, 10.1016/j.automatica.2004.06.001, Automatica 40 (2004), 1677-1687. Zbl1162.93353MR2155461DOI10.1016/j.automatica.2004.06.001
  18. J. H. Lü, S. M. Yu, H. Leung, G. R. Chen, 10.1109/TCSI.2005.854412, IEEE Trans. Circuits Systems - I: Regular Papers 53 (2006), 149-165. DOI10.1109/TCSI.2005.854412
  19. G. Maione, P. Lino, 10.1007/s11071-006-9125-x, Nonlinear Dynamics 49 (2007), 251-257. DOI10.1007/s11071-006-9125-x
  20. D. Matignon, Stability result on fractional differential equations with applications to control processing., In: Proc. IMACS-SMC (IMACS-SMC), Lille 1996, pp. 963-968. 
  21. T. Menacer, N. Hamri, Synchronization of different chaotic fractional-order systems via approached auxiliary system the modified Chua oscillator and the modified Van der Pol-Duffing oscillator., Electr. J. Theoret. Phys. 8 (2011), 253-266. 
  22. K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations., John Wiley and Sons, New York 1993. Zbl0789.26002MR1219954
  23. C. A. Monje, V. Feliu, The fractional-order lead compensator., In: IEEE International Conference on Computational Cybernetics (ICCC), Vienna 2004, pp. 347-352. 
  24. C. A. Monje, B. M. Vinagre, V. Feliu, Y. Q. Chen, Tuning and auto-tuning of fractional order controllers for industry applications., Control Engrg. Practice 16 (2008),798-812. 
  25. G. J. Penga, Y. L. Jiang, 10.1016/j.physleta.2008.01.061, Phys. Lett. A 372 (2008), 3963-3970. MR2418398DOI10.1016/j.physleta.2008.01.061
  26. G. J. Penga, Y. L. Jiang, F. Chen, 10.1016/j.physa.2008.02.057, Physica A 387 (2008), 3738-3746. DOI10.1016/j.physa.2008.02.057
  27. M. A. Savi, Chaos and order in biomedical rhythms., J. Brazil. Soc. Mechan. Sci. Engrg. 27 (2005), 157-169. 
  28. D. V. Senthilkumar, M. Lakshmanan, J. Kurths, 10.1103/PhysRevE.74.035205, Phys. Rev. E 74 (2006), 035205. DOI10.1103/PhysRevE.74.035205
  29. K. S. Tang, G. Q. Zhong, G. Chen, K. F. Man, Generation of N-scroll attractors via Sine function., IEEE Trans. Circuits and Systems - I: Fundamental Theory Appl. 48 (2001), 1369-1372. MR1854958
  30. M. S. Tavazoei, M. Haeri, S. Bolouki, M. Siami, 10.1007/s11071-008-9353-3, Nonlinear Dynamics 55 (2009), 179-190. Zbl1220.70025MR2466113DOI10.1007/s11071-008-9353-3
  31. L. A. B. Torres, L. A. Aguirre, 10.1016/j.physd.2004.06.006, Physica D 196 (2004), 387-406. Zbl1069.34057MR2090359DOI10.1016/j.physd.2004.06.006
  32. R. S. Varga, Matrix Iterative Analysis., Springer, Berlin 2000. Zbl1216.65042MR1753713
  33. H. U. Voss, 10.1103/PhysRevLett.87.014102, Phys. Rev. Lett. 87 (2001), 014102. DOI10.1103/PhysRevLett.87.014102
  34. Z. Wang, Y. T. Wu, Y. X. Li, Y. J. Zou, Adaptive backstepping control of a nonlinear electromechanical system with unknown parameters., In: Proc. 4th International Conference on Computer Science and Education (ICCSE), Nanning 2009, pp. 441-444. 
  35. Z. Wang, Y. T. Wu, Y. J. Zou, Analysis and sliding control of multi-scroll jerk circuit chaotic system., J. Xi'an University of Science and Technology 29 (2009), 765-768. 
  36. T. Yang, L. O. Chua, 10.1142/S0218127499000092, Internat. J. Bifurcation Chaos 9 (1999), 215-219. MR1689607DOI10.1142/S0218127499000092
  37. R. Zhang, Z. Y. Xu, S. X. Yang, X. M. He, 10.1016/j.chaos.2006.10.050, Chaos, Solitons Fractals 38 (2008), 97-105. MR2417647DOI10.1016/j.chaos.2006.10.050
  38. P. Zhou, X. F. Cheng, N. Y. Zhang, 10.1088/0253-6102/50/4/27, Commun. Theoret. Phys. 50 (2008), 931-934. DOI10.1088/0253-6102/50/4/27

Citations in EuDML Documents

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  1. Hamed Tirandaz, Chaos synchronization of TSUCS unified chaotic system, a modified function projective control method
  2. Zhen Wang, Wei Sun, Zhouchao Wei, Xiaojian Xi, Dynamics analysis and robust modified function projective synchronization of Sprott E system with quadratic perturbation
  3. Quanjun Wu, Hua Zhang, Drive network to a desired orbit by pinning control
  4. Mihua Ma, Hua Zhang, Jianping Cai, Jin Zhou, Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch
  5. Ke Ding, Qing-Long Han, Synchronization of two coupled Hindmarsh-Rose neurons

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