Robust synchronization of incommensurate fractional-order chaotic systems via second-order sliding mode technique

Journal of Applied Mathematics

Volumn 2013, Issue , 2013, Pages

  Chen, Hua ^a   Chen, Wen ^b   Zhang, Binwu ^a   Cao, Haitao ^a  

^a HOHAI UNIVERSITY   (China)

^b HOHAI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84881466704     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2013/321253     Document Type: Article

References (48)

1. Podlubny I., Fractional Differential Equations 1999 New York, NY, USA Academic Press MR1658022 ZBL1056.93542
2. Hilfer R., Application of Fractional Calculus in Physics 2000 Singapore World Science Publishing
3. Ortigueira M. D., Tenreiro Machado J. A., Fractional signal processing and applications. Signal Processing 2003 83 11 2285 2286 2-s2.0-0141892682 10.1016/S0165-1684(03)00181-6
4. Lanusse P., Benlaoukli H., Nelson-Gruel D., Oustaloup A., Fractional-order control and interval analysis of SISO systems with time-delayed state. IET Control Theory & Applications 2008 2 1 16 23 10.1049/iet-cta:20060491 MR2384751 (Pubitemid 351169605)
5. http://mechatronics.ece.usu.edu/foc/cdc02tw/cdrom/Lectures/AppendixB/ appendixB.pdf
6. Petráš I., Tuning and implementation methods for fractional-order controllers. Fractional Calculus and Applied Analysis 2012 15 2 282 303 10.2478/s13540-012-0021-4 MR2897780
7. Dorcak L., Numerical models for the simulation of the fractional-order control systems. 2002, http://arxiv.org/abs/math/0204108v1
8. Oldham K. B., Spanier J., The Fractional Calculus 1974 New York, NY, USA Academic Press MR0361633
9. Mandelbrot B. B., Van Ness J. W., Fractional Brownian motions, fractional noises and applications. SIAM Review 1968 10 422 437 MR0242239 10.1137/1010093 ZBL0179.47801
10. Engheta N., On fractional calculus and fractional multipoles in electromagnetism. IEEE Transactions on Antennas and Propagation 1996 44 4 554 566 10.1109/8.489308 MR1382017 ZBL0944.78507 (Pubitemid 126780696)
11. Baleanu D., Golmankhaneh A. K., Nigmatullin R., Golmankhaneh A. K., Fractional Newtonian mechanics. Central European Journal of Physics 2010 8 1 120 125 2-s2.0-71949100439 10.2478/s11534-009-0085-x
12. Sun H. G., Chen W., Wei H., Chen Y. Q., A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems. European Physical Journal 2011 193 1 185 192 2-s2.0-79953691444 10.1140/epjst/e2011-01390-6
13. Sun H., Chen Y., Chen W., Random-order fractional differential equation models. Signal Processing 2011 91 3 525 530 2-s2.0-78049351606 10.1016/j.sigpro.2010.01.027
14. Chen W., Lin J., Wang F., Regularized meshless method for nonhomogeneous problems. Engineering Analysis with Boundary Elements 2011 35 2 253 257 10.1016/j.enganabound.2010.08.010 MR2740350 ZBL1259.65200
15. Oustaloup A., La Derivation Non Entiere: Theorie. Synthese et Application S 1995 Paris, France Editions Hermes
16. Magin R. L., Fractional calculus in bioengineering, part 3. Critical Reviews in Biomedical Engineering 2004 32 3-4 195 377 2-s2.0-11144305217 10.1615/CritRevBiomedEng.v32.i34.10 (Pubitemid 40024065)
17. Podlubny I., Fractional-order systems and P I D -controllers. IEEE Transactions on Automatic Control 1999 44 1 208 214 10.1109/9.739144 MR1666937
18. Tavazoei M. S., Haeri M., Jafari S., Bolouki S., Siami M., Some applications of fractional calculus in suppression of chaotic oscillations. IEEE Transactions on Industrial Electronics 2008 55 11 4094 4101 2-s2.0-56349146591 10.1109/TIE.2008.925774
19. Linares H., Baillot C., Oustaloup A., Ceyral C., Generation of a fractional ground: application in robotics. Proceedings of the International Congress IEE-Smc (CESA '96) July 1996 Lille, France
20. Duarte F. B. M., Tenreiro Machado J. A., Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators. Nonlinear Dynamics 2002 29 1-4 315 342 10.1023/A:1016559314798 MR1926478 ZBL1027.70011 (Pubitemid 34945404)
21. Li C., Chen G., Chaos in the fractional order Chen system and its control. Chaos, Solitons & Fractals 2004 22 3 549 554 2-s2.0-2042470796 10.1016/j.chaos.2004.02.035
22. Sheu L.-J., Chen H.-K., Chen J.-H., Tam L.-M., Chen W.-C., Lin K.-T., Kang Y., Chaos in the Newton-Leipnik system with fractional order. Chaos, Solitons & Fractals 2008 36 1 98 103 10.1016/j.chaos.2006.06.013 MR2372049 ZBL1152.37319 (Pubitemid 47576640)
23. Ahmad W. M., Sprott J. C., Chaos in fractional-order autonomous nonlinear systems. Chaos, Solitons & Fractals 2003 16 2 339 351 2-s2.0-0037332868 10.1016/S0960-0779(02)00438-1 (Pubitemid 35412185)
24. Grigorenko I., Grigorenko E., Chaotic dynamics of the fractional Lorenz system. Physical Review Letters 2003 91 3 4 034101 2-s2.0-0041384356
25. Danca M.-F., Chaotic behavior of a class of discontinuous dynamical systems of fractional-order. Nonlinear Dynamics 2010 60 4 525 534 10.1007/s11071-009-9612-y MR2658530 ZBL1194.93087
26. Asheghan M. M., Beheshti M. T. H., Tavazoei M. S., Robust synchronization of perturbed Chen's fractional-order chaotic system. Communications in Nonlinear Science and Numerical Simulation 2011 16 1044 1051 10.1016/j.cnsns.2010.08.032 MR2765216
27. Aghababa M. P., Khanmohammadi S., Alizadeh G., Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Applied Mathematical Modelling 2011 35 6 3080 3091 10.1016/j.apm.2010.12.020 MR2776263 ZBL1219.93023
28. Zhang R., Yang S., Stabilization of fractional-order chaotic system via a single state adaptive-feedback controller. Nonlinear Dynamics 2012 68 1-2 45 51 10.1007/s11071-011-0202-4 MR2904155 ZBL1243.93099
29. Wang S., Yu Y. G., Generalized projective synchronization of fractional order chaotic systems with different dimensions. Chinese Physics Letters 2012 29 2 3 020505
30. Yin C., Dadras S., Zhang S. M., Chen Y. Q., Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach. Applied Mathematical Modelling 2013 37 4 1607 2600
31. Hosseinnia S. H., Ghaderi R., Ranjbar N. A., Mahmoudian M., Momani S., Sliding mode synchronization of an uncertain fractional order chaotic system. Computers & Mathematics with Applications 2010 59 5 1637 1643 10.1016/j.camwa.2009.08.021 MR2595936 ZBL1189.34011
32. Wu X. J., Lu H. T., Shen S. L., Synchronization of a new fractional-order hyperchaotic system. Physics Letters A 2009 373 27-28 2329 2337 10.1016/j.physleta.2009.04.063 MR2533122 ZBL1231.34091
33. Senejohnny D. M., Delavari H., Active sliding observer scheme based fractional chaos synchronization. Communications in Nonlinear Science and Numerical Simulation 2012 17 11 4373 4383 10.1016/j.cnsns.2012.03.004 MR2930340 ZBL1253.34056
34. Yin C., Dadras S., Zhong S.-M., Design an adaptive sliding mode controller for drive-response synchronization of two different uncertain fractional-order chaotic systems with fully unknown parameters. Journal of the Franklin Institute 2012 349 10 3078 3101 10.1016/j.jfranklin.2012.09.009 MR2998646 ZBL1255.93038
35. Chen D.-Y., Liu Y.-X., Ma X.-Y., Zhang R.-F., Control of a class of fractional-order chaotic systems via sliding mode. Nonlinear Dynamics 2012 67 1 893 901 10.1007/s11071-011-0002-x MR2869246 ZBL1242.93027
36. Wu X. J., Lai D. R., Lu H. T., Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes. Nonlinear Dynamics 2012 69 1-2 667 683 10.1007/s11071-011-0295-9 MR2929901 ZBL1258.34130
37. Bartolini G., Fridman L., Pisano A., Usai E., Modern Sliding Mode Control Theory. New Perspectives and Applications 2008 375 Berlin, Germany Springer Lecture Note in Control and Information Sciences 10.1007/978-3-540-79016-7 MR2435347
38. Levant A., Quasi-continuous high-order sliding-mode controllers. IEEE Transactions on Automatic Control 2005 50 11 1812 1816 10.1109/TAC.2005.858646 MR2182731 (Pubitemid 41748880)
39. Levant A., Principles of 2-sliding mode design. Automatica 2007 43 4 576 586 10.1016/j.automatica.2006.10.008 MR2306701 ZBL1261.93027 (Pubitemid 46341236)
40. Moreno J. A., Osorio M., A Lyapunov approach to second-order sliding mode controllers and observers. Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08) December 2008 2856 2861 2-s2.0-62949230418 10.1109/CDC.2008.4739356
41. Aghababa M. P., Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique. Nonlinear Dynamics 2012 69 1-2 247 261 10.1007/s11071-011-0261-6 MR2929869 ZBL1253.93016
42. Bhat S. P., Bernstein D. S., Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization 2000 38 3 751 766 10.1137/S0363012997321358 MR1756893 ZBL0945.34039
43. Pisano A., Rapaić M. R., Jeličić Z. D., Usai E., Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics. International Journal of Robust and Nonlinear Control 2010 20 18 2045 2056 10.1002/rnc.1565 MR2777532 ZBL1207.93079
44. Dadras S., Momeni H. R., Control of a fractional-order economical system via sliding mode. Physica A 2010 389 12 2434 2442 2-s2.0-77949913266 10.1016/j.physa.2010.02.025
45. Diethelm K., Ford N. J., Freed A. D., A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 2002 29 1-4 3 22 10.1023/A:1016592219341 MR1926466 ZBL1009.65049 (Pubitemid 34945390)
46. http://www.mathworks.com/matlabcentral/fileexchange/27336-fractional- order-chaotic-systems
47. Wang X.-Y., Song J.-M., Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control. Communications in Nonlinear Science and Numerical Simulation 2009 14 8 3351 3357 2-s2.0-60849138778 10.1016/j.cnsns.2009.01.010
48. Hegazi A. S., Matouk A. E., Dynamical behaviors and synchronization in the fractional order hyperchaotic Chen system. Applied Mathematics Letters 2011 24 11 1938 1944 10.1016/j.aml.2011.05.025 MR2812242 ZBL1234.34036