Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

Nonlinear Dynamics

Volumn 69, Issue 1-2, 2012, Pages 247-261

  Aghababa, Mohammad Pourmahmood ^a  

^a URMIA UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Finite time convergence; Fractional chaotic system; Fractional terminal sliding mode; Nonautonomous system; Uncertainty

Indexed keywords

FINITE-TIME CONVERGENCE; FRACTIONAL CHAOTIC SYSTEMS; NON-AUTONOMOUS SYSTEM; TERMINAL SLIDING MODE; UNCERTAINTY;

CHAOTIC SYSTEMS; CONTROL THEORY; UNCERTAINTY ANALYSIS;

UNMANNED AERIAL VEHICLES (UAV);

EID: 84861726301     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0261-6     Document Type: Article

References (58)

1. K.P. Wilkie C.S. Drapaca S. Sivaloganathan 2011 A nonlinear viscoelastic fractional derivative model of infant hydrocephalus Appl. Math. Comput. 217 8693 8704 2802278 1215.92036 10.1016/j.amc.2011.03.115
2. Y. Luo Y.Q. Chen Y. Pi 2011 Experimental study of fractional order proportional derivative controller synthesis for fractional order systems Mechatronics 21 204 214 10.1016/j.mechatronics.2010.10.004
3. J. Sabatier M. Cugnet S. Laruelle S. Grugeon B. Sahut A. Oustaloup J.M. Tarascon 2010 A fractional order model for lead-acid battery crankability estimation Commun. Nonlinear Sci. Numer. Simul. 15 1308 1317 10.1016/j.cnsns.2009.05.067
4. + T-cells Comput. Math. Appl. 62 996 1002 2824687 1228.92064 10.1016/j.camwa.2011.03.091
5. N. Laskin 2000 Fractional market dynamics Physica A 287 482 492 1802416 10.1016/S0378-4371(00)00387-3 (Pubitemid 32034792)
6. M. Rivero J.J. Trujillo L. Vàzquez M.P. Velasco 2011 Fractional dynamics of populations Appl. Math. Comput. 218 1089 1095 2831362 1226.92060 10.1016/j.amc.2011.03.017
7. J. Cao C. Ma Z. Jiang S. Liu 2011 Nonlinear dynamic analysis of fractional order rub-impact rotor system Commun. Nonlinear Sci. Numer. Simul. 16 1443 1463 10.1016/j.cnsns.2010.07.005
8. C. Ionescu J.T. Machado R. De Keyser 2011 Fractional-order impulse response of the respiratory system Comput. Math. Appl. 62 845 854 1228.65251 10.1016/j.camwa.2011.04.021
9. I.S. Jesus J.A.T. Machado 2008 Fractional control of heat diffusion systems Nonlinear Dyn. 54 263 282 1210.80008 10.1007/s11071-007-9322-2
10. M.R. Rapaić Z.D. Jeličić 2010 Optimal control of a class of fractional heat diffusion systems Nonlinear Dyn. 62 39 51 1210.35270 10.1007/s11071-010-9697-3
11. M.S. Tavazoei M. Haeri S. Bolouki M. Siami 2009 Using fractional-order integrator to control chaos in single-input chaotic systems Nonlinear Dyn. 55 179 190 2466113 1220.70025 10.1007/s11071-008-9353-3
12. H. Delavari A.N. Ranjbar R. Ghaderi S. Momani 2010 Fractional order control of a coupled tank Nonlinear Dyn. 61 383 397 2718300 1204.93086 10.1007/s11071-010-9656-z
13. M.P. Aghababa A. Heydari 2011 Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities Appl. Math. Model. 10.1016/j.apm.2011.09.023
14. M.P. Aghababa H.P. Aghababa 2011 Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties Nonlinear Dyn. 10.1007/s11071-011-0181-5
15. M. Pourmahmood S. Khanmohammadi G. Alizadeh 2011 Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller Commun. Nonlinear Sci. Numer. Simul. 16 2853 2868 2772300 1221.93131 10.1016/j.cnsns.2010.09.038
16. M.P. Aghababa S. Khanmohammadi G. Alizadeh 2011 Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique Appl. Math. Model. 35 3080 3091 2776263 1219.93023 10.1016/j.apm.2010.12.020
17. M.P. Aghababa H.P. Aghababa 2011 Adaptive finite-time stabilization of uncertain non-autonomous chaotic electromechanical gyrostat systems with unknown parameters Mech. Res. Commun. 38 500 505 10.1016/j.mechrescom.2011.06.005
18. M.P. Aghababa 2011 A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs Chin. Phys. B 20 090505 10.1088/1674-1056/20/9/090505
19. X. Wu H. Wang 2010 A new chaotic system with fractional order and its projective synchronization Nonlinear Dyn. 61 407 417 1204.37035 10.1007/s11071-010-9658-x
20. I. Petráš 2009 Chaos in the fractional-order Volta's system: modeling and simulation Nonlinear Dyn. 57 157 170 1176.34050 10.1007/s11071-008-9429-0
21. C. Zeng Q. Yang J. Wang 2011 Chaos and mixed synchronization of a new fractional-order system with one saddle and two stable node-foci Nonlinear Dyn. 65 457 466 2830822 10.1007/s11071-010-9904-2
22. Z. Wang Y. Sun G. Qi B.J. van Wyk 2010 The effects of fractional order on a 3-D quadratic autonomous system with four-wing attractor Nonlinear Dyn. 62 139 150 1209.34060 10.1007/s11071-010-9705-7
23. X.-Y. Wang J.-M. Song 2009 Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control Commun. Nonlinear Sci. Numer. Simul. 14 3351 3357 2483884 1221.93091 10.1016/j.cnsns.2009.01.010
24. A.S. Hegazi A.E. Matouk 2011 Dynamical behaviors and synchronization in the fractional order hyperchaotic Chen system Appl. Math. Lett. 24 1938 1944 2812242 1234.34036 10.1016/j.aml.2011.05.025
25. M.S. Tavazoei M. Haeri 2009 Describing function based methods for predicting chaos in a class of fractional order differential equations Nonlinear Dyn. 57 363 373 2520216 1176.34051 10.1007/s11071-008-9447-y
26. S. Balochian A.K. Sedigh M. Haeri 2011 Stabilization of fractional order systems using a finite number of state feedback laws Nonlinear Dyn. 66 141 152 2836605 10.1007/s11071-010-9916-y
27. S.E. Hamamci 2008 Stabilization using fractional-order PI and PID controllers Nonlinear Dyn. 51 329 343 1170.93023 10.1007/s11071-007-9214-5 (Pubitemid 47632368)
28. Z.M. Odibat 2010 Adaptive feedback control and synchronization of non-identical chaotic fractional order systems Nonlinear Dyn. 60 479 487 2658527 1194.93105 10.1007/s11071-009-9609-6
29. J. Hu Y. Han L. Zhao 2010 Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems Commun. Nonlinear Sci. Numer. Simul. 15 115 123 2567061 1221.37212 10.1016/j.cnsns.2009.03.017
30. G. Peng 2007 Synchronization of fractional order chaotic systems Phys. Lett. A 363 426 432 2287821 1197.37040 10.1016/j.physleta.2006.11.053
31. J.-W. Wang Y.-B. Zhang 2009 Synchronization in coupled nonidentical incommensurate fractional-order systems Phys. Lett. A 374 202 207 1235.34159 10.1016/j.physleta.2009.10.051
32. L. Pan W. Zhou J. Fang D. Li 2010 Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems Commun. Nonlinear Sci. Numer. Simul. 15 3754 3762 2652647 1222.34063 10.1016/j.cnsns.2010.01.025
33. M.M. Asheghan M.T.H. Beheshti M.S. Tavazoei 2011 Comments on "Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control" [Commun. Nonlinear Sci. Numer. Simul. 15, 3754-3762 (2010)] Commun. Nonlinear Sci. Numer. Simul. 16 2656 2657 2765216 1222.34060 10.1016/j.cnsns.2010.08.032
34. J.G. Lu 2006 Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal Physica A 359 107 118 10.1016/j.physa.2005.04.040 (Pubitemid 41526243)
35. Q.-S. Zhong J.-F. Bao Y.-B. Yu X.-F. Liao 2008 Impulsive control for fractional-order chaotic systems Chin. Phys. Lett. 25 2812 10.1088/0256-307X/25/ 8/022
36. ∞ synchronization of uncertain fractional order chaotic systems: Adaptive fuzzy approach ISA Trans. 50 548 556 10.1016/j.isatra.2011.06.001
37. ∞ synchronization of uncertain fractional order chaotic systems: Adaptive fuzzy approach" [ISA Trans 50, 548-556 (2011)] ISA Trans. 10.1016/j.isatra.2011.10.011
38. X. Wu H. Lu S. Shen 2009 Synchronization of a new fractional-order hyperchaotic system Phys. Lett. A 373 2329 2337 2533122 1231.34091 10.1016/j.physleta.2009.04.063
39. S. Bhalekar V. Daftardar-Gejji 2010 Synchronization of different fractional order chaotic systems using active control Commun. Nonlinear Sci. Numer. Simul. 15 3536 3546 2592631 1222.94031 10.1016/j.cnsns.2009.12.016
40. L. Song J. Yang S. Xu 2010 Chaos synchronization for a class of nonlinear oscillators with fractional order Nonlinear Anal. 72 2326 2336 2577800 1187.34066 10.1016/j.na.2009.10.033
41. L. Pan W. Zhou L.G. Zhou K. Sun 2011 Chaos synchronization between two different fractional-order hyperchaotic systems Commun. Nonlinear Sci. Numer. Simul. 16 2628 2640 2765214 1221.37220 10.1016/j.cnsns.2010.09.016
42. M.S. Tavazoei M. Haeri 2008 Synchronization of chaotic fractional-order systems via active sliding mode controller Physica A 387 57 70 2514122 10.1016/j.physa.2007.08.039 (Pubitemid 350051260)
43. S.H. Hosseinnia R. Ghaderi A. Ranjbar M. Mahmoudian S. Momani 2010 Sliding mode synchronization of an uncertain fractional order chaotic system Comput. Math. Appl. 59 1637 1643 2595936 1189.34011 10.1016/j.camwa.2009.08.021
44. C. Yin S.-M. Zhong W.-F. Chen 2012 Design of sliding mode controller for a class of fractional-order chaotic systems Commun. Nonlinear Sci. Numer. Simul. 17 356 366 2826014 10.1016/j.cnsns.2011.04.024
45. D.-Y. Chen Y.-X. Liu X.-Y. Ma R.-F. Zhang 2011 Control of a class of fractional-order chaotic systems via sliding mode Nonlinear Dyn. 10.1007/s11071-011-0002-x
46. R. Zhang S. Yang 2011 Adaptive synchronization of fractional-order chaotic systems via a single driving variable Nonlinear Dyn. 10.1007/s11071-011-9944-2
47. M.P. Aghababa 2012 Comments on "Design of sliding mode controller for a class of fractional-order chaotic systems" [Commun. Nonlinear Sci. Numer. Simul. 17, 356-366 (2012)] Commun. Nonlinear Sci. Numer. Simul. 17 1485 1488 2843812 10.1016/j.cnsns.2011.08.004
48. M.P. Aghababa 2011 Comments on "Adaptive synchronization of fractional-order chaotic systems via a single driving variable" [Nonlinear Dyn. (2011). doi:10.1007/s11071-011-9944-2] Nonlinear Dyn. 10.1007/s11071-011- 0216-y
49. M.P. Aghababa 2011 Comments on "Control of a class of fractional-order chaotic systems via sliding mode" [Nonlinear Dyn. (2011). doi:10.1007/s11071-011-0002-x] Nonlinear Dyn. 10.1007/s11071-011-0218-9
50. Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)
51. Y. Li Y.Q. Chen I. Podlubny 2009 Mittag-Leffler stability of fractional order nonlinear dynamic systems Automatica 45 1965 1969 1185.93062 10.1016/j.automatica.2009.04.003
52. Y. Li Y.Q. Chen I. Podlubny 2010 Stability of fractional order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability Comput. Math. Appl. 59 1810 1821 2595955 1189.34015 10.1016/j.camwa.2009.08.019
53. K. Diethelm N.J. Ford A.D. Freed 2002 A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 3 22 1926466 1009.65049 10.1023/A:1016592219341 (Pubitemid 34945390)
54. Utkin, V.I.: Sliding Modes in Control Optimization. Springer, Berlin (1992)
55. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)
56. X. Yu Z. Man 1998 Multi-input uncertain linear systems with terminal sliding-mode control Automatica 34 389 392 1623085 0915.93012 10.1016/S0005-1098(97)00205-7 (Pubitemid 128413982)
57. X. Yu Z. Man 2002 Fast terminal sliding-mode control design for nonlinear dynamical systems IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49 261 264 1890386 10.1109/81.983876 (Pubitemid 34291480)
58. Z.-M. Ge W.-R. Jhuang 2007 Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor Chaos Solitons Fractals 33 270 289 1152.34355 10.1016/j.chaos.2005.12.040 (Pubitemid 46209796)