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

Kybernetika

Volumn 48, Issue 2, 2012, Pages 190-205

  Liang, Hongtao ^a   Wang, Zhen ^b   Yue, Zongmin ^c   Lu, Ronghui ^a  

^a WUYI UNIVERSITY   (China)

^b XIJING UNIVERSITY   (China)

^c SHAANXI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Chaotic masking; Fractional chaotic systems; Fractional differential controller; Gershgorin circle theorem; GS; Pole assignment algorithm; SC; State observer

Indexed keywords

EID: 84859845956     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. M. A. Aon, S. Cortassa, and D. Lloyd: Chaotic dynamics and fractal space in biochemistry: Simplicity underlies complexity. Cell Biology Internat. 24 (2000), 581-587.
2. K. B. Arman, K. Fallahi, N. Pariz, and H. Leung: A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter. Comm. Nonlinear Sci. Numer. Simul. 14 (2009), 863-879.
3. S. Banerjee, D. Ghosh, and A. C. Roy: Multiplexing synchronization and its applications in cryptography. Physica Scripta 78 (2008), 015010.
4. A. Biswas, S. Das, A. Abraham, and S. Dasgupta: Design of fractional-order PIλDμ controllers with an improved differential evolution. Engrg. Appl. Artif. Intell. 22 (2009), 343-350.
5. A. Charef: Analogue realisation of fractional-order integrator, differentiator and fractional PIλDμ controller. Control Theory Appl. 153 (2006), 714-720. (Pubitemid 44563932)
6. A. Charef, H. H. Sun, Y. Y. Tsao, and B. Onaral: Fractal system as represented by singularity function. IEEE Trans. Automat. Control 37 (1992),1465-1470. (Pubitemid 23555835)
7. M. J. Chen, D.P. Li, and A. J. Zhang: Chaotic synchronization based on nonlinear stateobserver and its application in secure communication. J. Marine Sci. Appl. 3 (2004), 64-70.
8. G. Chen and X. Yu: Chaos Control: Theory and Applications. Springer, Berlin 2003.
9. K. Diethelm, N. J. Ford, and A. D. Freed: A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 29 (2002), 3-22. (Pubitemid 34945390)
10. K. Diethelm, N. J. Ford, and A. D. Freed: Detailed error analysis for a fractional Adams method. Numerical Algorithms 36 (2004), 31-52. (Pubitemid 39072748)
11. D. Ghosh: Nonlinear active observer-based generalized synchronization in time-delayed systems. Nonlinear Dynamics 59 (2010), 179-190.
12. R. M. Guerra and W. Yu: Chaotic synchronization and secure communication via slidingmode observer. Internat. J. Bifurcation Chaos 18 (2008), 235-243. (Pubitemid 351700591)
13. J. B. Hu, Y. Han, and L. D. Zhao: Synchronizing fractional chaotic systems based on Lyapunov equation. Acta Physica Sinica 57 (2008), 7522-7526.
14. J. B. Hu, Y. Han, and L. D. Zhao: Adaptive control the fractional unified chaotic system based on the estimated eigenvalue theory. J. Physics: Conference Series 96 (2008), 012151.
15. A.A. Koronovskii, O. I. Moskalenko, and A.E. Hramov: On the use of chaotic synchronization for secure communication. Physics-Uspekhi 52 (2009), 1213-1238.
16. J. H. Lü and G.R. Chen: Generating multi-scroll chaotic attractors: Theories, methods and applications. Internat. J. Bifurcation Chaos 16 (2006), 775-858.
17. J. H. Lü, G. R. Chen, X.H. Yu, and H. Leung: Design and analysis of multiscroll chaotic attractors from saturated function series. IEEE Trans. Circuits Systems - I: Regular Papers 51 (2003), 2476-2490. (Pubitemid 40009469)
18. J. H. Lü, G.R. Chen, and S.C. Zhang: The compound structure of a new chaotic attractor. Chaos, Solitons Fractals 14 (2002), 669-672.
19. J. H. Lü, F. L. Han, X. H. Yu, and G. R. Chen: Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method. Automatica 40 (2004), 1677-1687.
20. J. H. Lü, S. M. Yu, H. Leung, and G.R. Chen: Experimental verification of multidirectional multiscroll chaotic attractors. IEEE Trans. Circuits Systems - I: Regular Papers 53 (2006), 149-165. (Pubitemid 43141938)
21. G. Maione and P. Lino: New tuning rules for fractional PIα controllers. Nonlinear Dynamics 49 (2007), 251-257. (Pubitemid 46739713)
22. D. Matignon: Stability result on fractional differential equations with applications to control processing. In: Proc. IMACS-SMC (IMACS-SMC), Lille 1996, pp. 963-968.
23. T. Menacer and 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.
24. K. S. Miller and B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley and Sons, New York 1993.
25. C. A. Monje and V. Feliu: The fractional-order lead compensator. In: IEEE International Conference on Computational Cybernetics (ICCC), Vienna 2004, pp. 347-352.
26. C. A. Monje, B. M. Vinagre, V. Feliu, and Y.Q. Chen: Tuning and auto-tuning of fractional order controllers for industry applications. Control Engrg. Practice 16 (2008),798-812. (Pubitemid 351470859)
27. G. J. Penga and Y. L. Jiang: Generalized projective synchronization of a class of fractionalorder chaotic systems via a scalar transmitted signal. Phys. Lett. A 372 (2008), 3963-3970.
28. G. J. Penga, Y. L. Jiang, and F. Chen: Generalized synchronization of fractional order chaotic systems. Physica A 387 (2008), 3738-3746.
29. M. A. Savi: Chaos and order in biomedical rhythms. J. Brazil. Soc. Mechan. Sci. Engrg. 27 (2005), 157-169. (Pubitemid 40860543)
30. D. V. Senthilkumar, M. Lakshmanan, and J. Kurths: Phase synchronization in time-delay systems. Phys. Rev. E 74 (2006), 035205.
31. K. S. Tang, G.Q. Zhong, G. Chen, and K. F. Man: Generation of N-scroll attractors via Sine function. IEEE Trans. Circuits and Systems - I: Fundamental Theory Appl. 48 (2001), 1369-1372. (Pubitemid 33120592)
32. M. S. Tavazoei, M. Haeri, S. Bolouki and M. Siami: Using fractional-order integrator to control chaos in single-input chaotic systems. Nonlinear Dynamics 55 (2009), 179-190.
33. L. A. B. Torres and L.A. Aguirre: Transmitting information by controlling nonlinear oscillators. Physica D 196 (2004), 387-406.
34. R. S. Varga: Matrix Iterative Analysis. Springer, Berlin 2000.
35. H.U. Voss: Dynamic long-term anticipation of chaotic states. Phys. Rev. Lett. 87 (2001), 014102.
36. Z. Wang, Y. T. Wu, Y. X. Li, and 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.
37. Z. Wang, Y.T. Wu, and 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.
38. T. Yang and L. O. Chua: Generalized synchronization of chaos via linear transforms. Internat. J. Bifurcation Chaos 9 (1999), 215-219. (Pubitemid 129341040)
39. R. Zhang, Z. Y. Xu, S. X. Yang, and X. M. He: Generalized synchronization via impulsive contro. Chaos, Solitons Fractals 38 (2008), 97-105. (Pubitemid 351503970)
40. P. Zhou, X. F. Cheng, and N. Y. Zhang: Generalized synchronization between different fractional-order chaotic systems. Commun. Theoret. Phys. 50 (2008), 931-934.