Adaptive synchronization of the fractional-order chaotic systems with unknown parameters

Proceedings - International Conference on Electrical and Control Engineering, ICECE 2010

Volumn , Issue , 2010, Pages 351-355

  Yin, Ke ^a   Chu, Yanping ^a  

^a HENAN UNIVERSITY   (China)

Author keywords

Adaptive control; Parameter identification; Synchronization; The fractional order system

Indexed keywords

ADAPTIVE CONTROL; ADAPTIVE CONTROLLERS; ADAPTIVE SYNCHRONIZATIONS; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; NUMERICAL SIMULATION; PARAMETER IDENTIFICATION; STABILITY THEORIES; UNKNOWN PARAMETERS;

CHAOTIC SYSTEMS; CONTROL THEORY; ELECTRICAL ENGINEERING; PARAMETER ESTIMATION; SYNCHRONIZATION;

ADAPTIVE CONTROL SYSTEMS;

EID: 79952214304     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/iCECE.2010.93     Document Type: Conference Paper

References (24)

1. I. Podlubny, "Fractional Differential Equations", New York: Academic Press, 1999.
2. R. Hifer, "Applications of Fractional Calculus in Physics", New Jersey: World Scientific, 2001.
3. R.C. Koeller, "Application of fractional calculus to the theory of viscoelasticity", J. Appl. Mech., vol. 51, pp. 299-307, June 1984. (Pubitemid 14583151)
4. H.H. Sun, A.A. Abdelwahad, B. Onaral, "Linear approximation of transfer function with a pole of fractional order", IEEE Trans. Automat. Control, vol. 29, pp. 441-444, May 1984. (Pubitemid 14588227)
5. M. Ichise, Y. Nagayanagi, T. Kojima, "An analog simulation of noninteger order transfer functions for analysis of electrode process", J. Electroanal. Chem., vol.33, pp. 253-265, 1971.
6. O. Heaviside, "Electromagnetic Theory", New York: Chelsea, 1971.
7. N. Laskin, "Fractional market dynamics", Physica A, vol. 287, pp. 482-492, December 2000. (Pubitemid 32034792)
8. D. Kunsezov, A. Bulagc, G.D. Dang, "Quantum levy processes and fractional kinetics", Phys. Rev. Lett., vol. 82, pp. 1136-1139, 1999. (Pubitemid 129583696)
9. I. Grigorenko, E. Grigorenko, "Chaotic dynamics of the fractional Lorenz system", Phys. Rev. Lett., vol. 91, pp. 034101, July 2003.
10. C.G. Li, G. Chen, "Chaos and hyperchaos in the fractional-order Rössler equations", Physica A, vol. 341, pp. 55-61, October 2004.
11. T.T. Hartley, C.F. Lorenzo, H.K. Qammer, "Chaos in a fractional order Chua's system", IEEE Trans. Circuits Syst.-I, vol. 42, pp. 485-490, August 1995.
12. P. Arena, R. Caponetto, L. Fortuna, D. Porto, "Chaos in a fractional order Duffing system", Proceedings of European Conference on Circuit Theory and Design, Budapest, September 1997, pp. 1259-1262.
13. C.P. Li, G.J. Peng, "Chaos in Chen's system with a fractional order", Chaos Solitons & Fractals, vol. 22, pp. 443-450, October 2004.
14. X. Wu, Y. Lu, "Generalized projective synchronization of the fractional-order Chen hyperchaotic system", Nonlinear Dyn., vol. 57, pp. 25-35, July 2009.
15. C.G. Li, X.F. Liao, J.B. Yu, "Synchronization of fractional order chaotic systems", Phys. Rev. E, vol. 68, pp. 067203, December 2003.
16. J.B. Hu, Y. Han, L.D. Zhao, "Synchronizing fractional chaotic systems based on Lyapunov equation", Acta Phy. Sin., vol. 57, pp. 7522-7526, December 2008.
17. X. Wu, J. Li, G. Chen. "Chaos in the fractional order unified system and its synchronization", J. Franklin Institute, vol. 345, pp. 392-401, July 2008.
18. G. Peng, Y. Jiang, F. Chen, "Generalized projective synchronization of fractional order chaotic systems", Physica A, vol. 387, pp. 3738-3746, May 2008.
19. J.W. Wang, Y.B. Zhang, "Synchronization in coupled nonidentical incommensurate fractional-order systems", Phys. Lett. A, vol. 374, pp. 202-207, December 2009.
20. H. Zhu, S. Zhou, Z. He, "Chaos synchronization of the fractional-order Chen's system", Chaos Solitons & Fractals, vol. 41, pp. 2733-2740, September 2009.
21. X. Wu, H. Lu, S. Shen, "Synchronization of a new fractional-order hyperchaotic system", Phys. Lett. A, vol. 373, pp. 2329-2337, June 2009.
22. J.H. Ma, Y.S. Chen, "Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system", Appl. Math. Mech., vol. 22, pp. 1375-1382, November 2001.
23. W.C. Chen, "Nonlinear dynamics and chaos in a fractional-order financial system", Chaos Solitons and Fractals, vol. 36, pp. 1305-1314, June 2008.
24. K. Diethelm, N.J. Ford, A.D. Freed, "A predictor-corrector approach for the numerical solution of fractional differential equations", Nonlinear Dyn., vol. 29, pp. 3-22, July 2002. (Pubitemid 34945390)