Synchronization of uncertain fractional-order chaotic systems via a novel adaptive controller. (English) Zbl 1539.34062
Summary: This paper deals with the drive-response synchronization scheme for uncertain fractional-order chaotic systems. Some novel sufficient conditions for chaos synchronization of fractional-order chaotic systems with model uncertainties and external disturbances are derived by using the fractional-order extension of the Lyapunov stability theorem. The designed synchronization are new, simple and yet easily realized experimentally compared with those where complex control functions are used. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.
MSC:
| 34H10 | Chaos control for problems involving ordinary differential equations |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
References:
| [1] | Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824, (1990) · Zbl 0938.37019 |
| [2] | El-Gohary, A.; Yassen, R., Adaptive control and synchronization of a coupled dynamic system with uncertain parameters, Chaos Solitons Fractals, 29, 1085-1094, (2006) · Zbl 1142.93422 |
| [3] | Hammamia, S.; Benrejeba, M.; Fekib, M.; Borne, P., Feedback control design for Rössler and Chen chaotic systems anti-synchronization, Phys. Lett. A, 374, 2835-2840, (2010) · Zbl 1237.34089 |
| [4] | Ojo, K. S.; Njah, A. N., A new active control method for control and tracking of chaotic systems, Afr. J. Math. Phys., 9, 59-71, (2010) · Zbl 1353.34074 |
| [5] | 043114. · Zbl 1317.93114 |
| [6] | 040704 · Zbl 07845092 |
| [7] | Faieghi, M. R.; Delavari, H., Chaos in fractional-order Genesio Tesi system and its synchronization, Commun. Nonlinear Sci. Numer. Simul., 17, 731-741, (2012) · Zbl 1239.93020 |
| [8] | 023130. · Zbl 1331.34129 |
| [9] | Yin, C.; Cheng, Y. H.; Chen, Y. Q.; Stark, B.; Zhong, S. M., Adaptive fractional-order switching-type control method design for 3d fractional-order nonlinear systems, Nonlinear Dyn., 82, 39-52, (2015) · Zbl 1348.93216 |
| [10] | Feng, M. K.; Wang, X. Y.; Wei, Q., Adaptive robust synchronization of fractional-order chaotic system with disturbance, J. Vib. Control, 21, 2259-2265, (2015) |
| [11] | Li, C. L.; Zhang, M.; Zhou, F.; Yang, X. B., Projective synchronization for a fractional-order chaotic system via single sinusoidal coupling, Optik, 127, 2830-2836, (2016) |
| [12] | Kilbas, A.; Srivastava, H.; Trujillo, J., Theory and Applications of Fractional Differential Equations, (2006), Elsevier · Zbl 1092.45003 |
| [13] | Aguila-Camacho, N.; Manuel, A.; Duarte-Mermoud, J.; Gallegos, A., Lyapunov functions for fractional order systems, Commun. Nonlinear Sci. Numer. Simul., 19, 2951-2957, (2014) · Zbl 1510.34111 |
| [14] | Khalil, H. K., Nonlinear Systems, (2002), Prentice Hall · Zbl 1003.34002 |
| [15] | Li, Y.; Chen, Y.; Podlubny, I., Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Comput. Math. Appl., 59, 1810-1821, (2010) · Zbl 1189.34015 |
| [16] | Chen, W. C., Nonlinear dynamics and chaos in a fractional-order financial system, Chaos Solitons Fractals, 36, 1305-1314, (2008) |
| [17] | 103128 · Zbl 1374.94779 |
| [18] | Dadras, S.; Momeni, H. R., Control of a fractional-order economical system via sliding mode, Physica A, 389, 2434-2442, (2010) |
| [19] | Wanga, Z.; Huang, X.; Shen, H., Control of an uncertain fractional order economic system via adaptive sliding mode, Neurocomputing, 83, 83-88, (2012) |
| [20] | 030504 |
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