Complete synchronization of commensurate fractional order chaotic systems using sliding mode control

Mechatronics

Volumn 23, Issue 7, 2013, Pages 873-879

  Razminia, Abolhassan ^a   Baleanu, Dumitru ^b,c,d  

^a PERSIAN GULF UNIVERSITY   (Iran)

^b CANKAYA UNIVERSITY   (Turkey)

^c INSTITUTE OF SPACE SCIENCES   (Romania)

^d KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

Chaotic systems; Complete synchronization; Fractional order dynamics; Sliding mode control

Indexed keywords

CHAOTIC SYSTEMS; SYNCHRONIZATION;

COMPLETE SYNCHRONIZATION; FRACTIONAL ORDER; FRACTIONAL-ORDER CHAOTIC SYSTEMS; POWER ELECTRONIC SYSTEMS; SELF-SUSTAINED OSCILLATIONS; UNIDIRECTIONAL COUPLING;

SLIDING MODE CONTROL;

EID: 84886314616     PISSN: 09574158     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechatronics.2013.02.004     Document Type: Article

References (39)

1. E. Ott, C. Grebogi, and J.A. Yorke Controlling chaos Phys Rev Lett 65 1990 1196 1199
2. XRg Shi, and Z.L. Wang Adaptive added-order anti-synchronization of chaotic systems with fully unknown parameters Appl Math Comput 215 2009 1711 1717
3. F. Chen, and W. Zhang Stabilization of parameters perturbation chaotic system via adaptive backstepping technique Appl Math Comput 200 2008 101 109
4. J.H. Park, D.H. Ji, S.C. Won, and S.M. Lee Hinf synchronization of time-delayed chaotic systems Appl Math Comput 204 2008 170 177
5. A. Razminia, V.J. Majd, and D. Baleanu Chaotic incommensurate fractional order Rossler system: active control synchronization Adv Differ Equ 15 2011 1 12
6. C. Zhu Feedback control methods for stabilizing unstable equilibrium points in a new chaotic system Nonlinear Anal-Theor 71 2009 2441 2446
7. S. Li, j Qiu, H. Ji, K. Zhu, and J. Li Piezoelectric vibration control for all-clamped panel using DOB-based optimal control Mechatronics 21 2011 1213 1221
8. A. Fradkov, B. Andrievsky, and K. Boykov Control of the coupled double pendulums system Mechatronics 15 2005 1289 1303
9. H. Gritli, N. Khraief, and S. Belghith Chaos control in passive walking dynamics of a compass-gait model Commun Nonlinear Sci Numer Simulat 18 2013 2048 2065
10. C.A.K. Kwuimy, B. Nana, and P. Woafo Experimental bifurcations and chaos in a modified self-sustained macro electromechanical system J Sound Vib 329 2010 3137 3148
11. S.C. Chang Synchronization in a steer-by-wire vehicle dynamic system Int J Eng Sci 45 2007 628 643
12. H. Zhang, D. Liu, and Z. Wang Controlling chaos, suppression, synchronization and chaotification 2009 Springer
13. N.S. Pai, and H.T. Yau Suppression of chaotic behavior in horizontal platform systems based on an adaptive sliding mode control scheme Commun Nonlinear Sci Numer Simulat 16 2011 133 143
14. T. Yang A survey of chaotic secure communication systems Int J Comput Cogn 2 2004 81 130
15. Y.C. Hung, T.L. Liao, and J.J. Yan Adaptive variable structure control for chaos suppression of unified chaotic systems Appl Math Comput 209 2009 391 398
16. Z.M. Ge, and C.H. Yang Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control Chaos, Solitons Fract 42 2009 994 1002
17. A.L. Fradkov, and R.J. Evans Control of chaos: methods and applications in engineering Ann Rev Control 2005 33 56
18. Yu H, Zhong S, Agrawal RP. Mathematics analysis and chaos in an ecological model with an impulsive control strategy. Commun Nonlinear Sci Numer Simulat; in press, accessed 24.04.10.
19. D.Y. Chen, W.L. Zhao, X.Y. Ma, and R.F. Zhang No-chattering sliding mode control chaos in Hindmarsh-Rose neurons with uncertain parameters Comput Math Appl 61 2011 3161 3171
20. R. Hilfer Applications of fractional calculus in physics 2001 World Scientific Hackensack (NJ)
21. K.S. Miller, and B. Ross An introduction to the fractional calculus and fractional differential equations 1993 A Wiley-Interscience Publication, JohnWiley & Sons New York (NY, USA)
22. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and applications of fractional differential equations 2006 Elsevier Science Amsterdam
23. D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo Fractional calculus models and numerical methods (series on complexity, nonlinearity and chaos) 2012 World Scientific
24. C. Ionescu, and R. De Keyser Relations between fractional order model parameters and lung pathology in chronic obstructive pulmonary disease IEEE Trans Biomed Eng 56 4 2009 978 987
25. C. Ionescu, P. Segers, and R. DeKeyser Mechanical properties of the respiratory system derived from morphologic insight IEEE Trans Biomed Eng 56 4 2009 949 959
26. D. Baleanu, O.G. Mustafa, and R.P. Agarwal An existence result for a superlinear fractional differential equation Appl Math Lett 23 2010 1129 1132
27. D. Baleanu, J.A.T. Machado, and A. Luo Fractional dynamics and control 2012 Springer
28. S. Dadras, and H.R. Momeni A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors Phys Lett A 373 2009 3637 3642
29. C. Yin, S. Zhong, and W. Chen Design of sliding mode controller for a class of fractional-order chaotic systems Commun Nonlinear Sci Numer Simulat 17 2012 356 366
30. S.H. Hosseinnia, R. Ghaderi, A.N. Ranjbar, M. Mahmoudian, and S. Momani Sliding mode synchronization of an uncertain fractional order chaotic system Comput Math Appl 59 2010 1637 1643
31. M.S. Tavazoei, and M. Haeri Synchronization of chaotic fractional-order systems via active sliding mode controller Physics A 387 2008 57 70
32. C. Li, and W. Deng Remarks on fractional derivatives Appl Math Comput 187 2007 777 784
33. Y. Wang, and C. Li Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle? Phys Lett A 363 2007 414 419
34. Matignon D. Stability results for fractional differential equations with applications to control processing. In: Computational engineering in systems and application multi-conference, IMACS, IEEE-SMC Proceedings, vol. 2. Lille, France, July 1996. p. 963-8.
35. J.H.B. Deane, and D.C. Hamill Instability, sub harmonics and chaos in power electronic system IEEE Trans Power Electron 5 1990 260 268
36. K. Chakrabarty, G. Poddar, and S. Banerjee Bifurcation behavior of the buck converter IEEE Trans Power Electron 11 1999 439 447
37. N. Hemati Strange attractor in brushless DC motor IEEE Trans Circ Syst - I: Fund Theory Appl 41 1994 40 45
38. K. Chakrabarty, U. Kar, and S. Kundu Chaotic behavior in a DC series drive 2010 Indian Institute of Technology Roorkee
39. J.M. Rosario, D. Dumur, and J.A.T. Machado Control of a 6-DOF parallel manipulator through a mechatronic approach J Vib Control 13 2007 1431 1446