×

Feedback and adaptive control for the synchronization of Chen system via a single variable. (English) Zbl 1024.37053

Summary: This letter addresses control for the synchronization of chaotic Chen systems via a single variable. Two control approaches, namely a linear feedback controller and an adaptive controller, are investigated. In both cases sufficient conditions for the synchronization are obtained analytically. The control performances are verified by numerical simulations.

MSC:

37N35 Dynamical systems in control
93D21 Adaptive or robust stabilization
93D15 Stabilization of systems by feedback
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M05 Simulation of dynamical systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, G.; Dong, X., From Chaos to Order Methodologies, Perspectives, and Applications (1998), World Scientific: World Scientific Singapore
[2] Parmananda, P., Phys. Lett. A, 240, 55 (1998)
[3] Agiza, H. N.; Yassen, M. T., Phys. Lett. A, 278, 191 (2001)
[4] Ma, W.; Yu, L., Jilin Normal College Transaction, 18, 30 (1997)
[5] Celka, P., IEEE Trans. Circuits Systems, 42, 455 (1995)
[6] Masoller, C., Physica A, 295, 301 (2001)
[7] Liao, T.-L.; Lin, S.-H., J. Franklin Inst., 336, 925 (1999)
[8] Liao, T.-L.; Tsai, S.-H., Chaos Solitons Fractals, 11, 1387 (2000)
[9] Wang, C.; Ge, S. S., Chaos Solitons Fractals, 12, 1199 (2001)
[10] Yang, T.; Chua, L. O., IEEE Trans. Circuits Systems, 44, 976 (1997)
[11] Yang, T.; Yang, L.-B.; Yang, C.-M., Physica D, 110, 18 (1997)
[12] J.A.K. Suykens, T. Yang, J. Vandewalle, L.O. Chua, in: Proceedings of the 37th IEEE, Conference on Decision and Control, 1998, p. 1963; J.A.K. Suykens, T. Yang, J. Vandewalle, L.O. Chua, in: Proceedings of the 37th IEEE, Conference on Decision and Control, 1998, p. 1963
[13] Xie, W.; Wen, C.; Li, Z., Phys. Lett. A, 275, 67 (2000)
[14] Itoh, M.; Yang, T.; Chua, L. O., Int. J. Bifur. Chaos, 11, 551 (2001)
[15] Chen, G.; Uet, T., Int. J. Bifur. Chaos, 9, 1465 (1999)
[16] Ogorzalek, M. J., IEEE Trans. Circuits Systems, 40, 693 (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.