Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

• Authors: Hadi Delavari , Danial Senejohnny , Dumitru Baleanu
• Languages of publication: EN

Abstracts

EN

In this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.

Keywords

EN

chaos synchronization; fractional calculus; sliding observer; finite hitting time

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 5
• Pages: 1095-1101

Dates

published

1 - 10 - 2012

online

21 - 11 - 2012

Contributors

author

Hadi Delavari

• Department of Electrical Engineering, Hamedan University of Technology, Hamedan, 65155, Iran

author

Danial Senejohnny

• Young Researchers club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

author

Dumitru Baleanu

References

• [1] E. Goldfain, Commun. Nonlinear Sci. 13, 1397 (2008) http://dx.doi.org/10.1016/j.cnsns.2006.12.007[Crossref]
• [2] G. M. Zaslavsky, Phys. Rep. 371, 461 (2002) http://dx.doi.org/10.1016/S0370-1573(02)00331-9[Crossref]
• [3] A. Piryatinska, A. I. Saichev, W. A. Woyczynski, Physica A 349, 375 (2005) http://dx.doi.org/10.1016/j.physa.2004.11.003[Crossref]
• [4] W. Chen, S. Holm, J. Acoust. Soc. Am. 115, 1424 (2004) http://dx.doi.org/10.1121/1.1646399[Crossref]
• [5] T. F. Nonnenmacher, In: Lecture Notes in Physics 381 (Springer, Berlin, 1991) 309
• [6] H. Weitzner, G. M. Zaslavsky, Commun. Nonlinear Sci. 8, 273 (2003) http://dx.doi.org/10.1016/S1007-5704(03)00049-2[Crossref]
• [7] N. Laskin, Phys. Rev. E 66, 056108 (2002) http://dx.doi.org/10.1103/PhysRevE.66.056108[Crossref]
• [8] E. Goldfain, Chaos Soliton. Fract. 19, 209 (2004) http://dx.doi.org/10.1016/S0960-0779(03)00304-7[Crossref]
• [9] E. Goldfain, Chaos Soliton. Fract. 23, 701 (2005) http://dx.doi.org/10.1016/j.chaos.2004.05.020[Crossref]
• [10] I. Podlubny, Fract. Calc. Appl. Anal. 5, 1 (2002)
• [11] E. M. Rabei, I. Almayteh, S. I. Muslih, D. Baleanu, Phys. Scripta 77, 015101 (2008) http://dx.doi.org/10.1088/0031-8949/77/01/015101[Crossref]
• [12] D. Baleanu, S. I. Muslih, Phys. Scripta 72, 119 (2008) http://dx.doi.org/10.1238/Physica.Regular.072a00119[Crossref]
• [13] E. Bai, K. Lonngren, J. Sprott, Chaos Soliton. Fract. 13, 1515 (2002) http://dx.doi.org/10.1016/S0960-0779(01)00160-6[Crossref]
• [14] Q. Zhang, S. Chen, Y. Hu, C. Wang, Physica A 371 (2006)
• [15] L. M. Pecora, T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990) http://dx.doi.org/10.1103/PhysRevLett.64.821[Crossref]
• [16] J. L. Mata-Machuca, R. Martinez-Guerra, R. Aguilar-Lopez, Commun. Nonlinear Sci. 15, 4114 (2010) http://dx.doi.org/10.1016/j.cnsns.2010.01.040[Crossref]
• [17] M. Feki, Phys. Lett. A 309, 53 (2003) http://dx.doi.org/10.1016/S0375-9601(03)00171-3[Crossref]
• [18] J. S. Lin, J. J. Yan, T. L. Liao, Chaos Soliton. Fract. 24, 597 (2005) http://dx.doi.org/10.1016/j.chaos.2004.09.031[Crossref]
• [19] A. Rodriguez, J. De Leon, L. Fridman, Chaos Soliton. Fract. 42, 3219 (2009) http://dx.doi.org/10.1016/j.chaos.2009.04.055[Crossref]
• [20] W. Yoo, D. Ji, S. Won, Phys Lett A. 374, 1354 (2010) http://dx.doi.org/10.1016/j.physleta.2010.01.023[Crossref]
• [21] K. E. Starkov, L. N. Coria, L. T. Aguilar, Commun. Nonlinear Sci. 17, 17 (2012) http://dx.doi.org/10.1016/j.cnsns.2011.04.020[Crossref]
• [22] W. H. Deng, C. P. Li, Physica A 353, 61 (2005) http://dx.doi.org/10.1016/j.physa.2005.01.021[Crossref]
• [23] J. Yan, C. P. Li, Chaos, Soliton. Fract. 32, 751 (2007) http://dx.doi.org/10.1016/j.chaos.2005.11.062[Crossref]
• [24] V. D. Gejji, S. Bhalekar, Comput. Appl. Math. 59, 1117 (2010) http://dx.doi.org/10.1016/j.camwa.2009.07.003[Crossref]
• [25] K. B. Oldham, J. Spanier, The fractional calculus (Academic Press, New York and London, 1974)
• [26] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993)
• [27] I. Podlubny, Fractional differential equations (Academic Press, California, 1999)
• [28] R. Hilfer, Application of Fractional Calculus in Physics (World Scientific, New Jersey, 2000) http://dx.doi.org/10.1142/9789812817747[Crossref]
• [29] M. O. Efe, IEEE T. Syst. Man Cy. B 38, 1561 (2008) http://dx.doi.org/10.1109/TSMCB.2008.928227[Crossref]
• [30] B. M. Vinagre, A. J. Calderon, In: Proc. 7th CONTROLO, Sep. 11–13, 2006, Lisbon, Portugal
• [31] P. Brunovsky, Kybernetika 6, 176 (1970) http://dx.doi.org/10.1007/BF00273963[Crossref]
• [32] S. Derivire, M.A. Aziz Alaoui, Le Havre, France, (2001)
• [33] M. Shahiri, R. Ghaderi, A. Ranjbar, S.H. Hosseinnia, S. Momani, Commun. Nonlinear Sci. 15 (2010)
• [34] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006)
• [35] M. S. Tavazoei, M. Haeri, IET Signal Process. 4 (2007)
• [36] Z. Shuqin, Nonlinear Analysis. 71 (2009)
• [37] G. S. Ladde, V. Lakshmikantham, A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations (Pitman Pub. Co., Boston, 1985)
• [38] B. Ahmad, S. Sivasundaram, Comput. Appl. Math. 197, 515 (2008) http://dx.doi.org/10.1016/j.amc.2007.07.065[Crossref]
• [39] D. M. Senejohnny, H. Delavari, Commun. Nonlinear Sci. (2012)
• [40] D. M. Senejohnny, H. Delavari, Signal, Image and Video Processing, (2012)

Identifiers

DOI

10.2478/s11534-012-0073-4