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Observer-based control for full-state projective synchronization of a general class of chaotic maps in any dimension. (English) Zbl 1123.37326

Summary: An observer-based control approach is proposed for generating and manipulating projective synchronization of a general class of chaotic maps in any dimension. The proposed approach overcomes some limitations in extent work, capable to execute the control for chaotic systems without restriction of partial-linearity, achieve a full-state synchronization and manipulate the outcome of the synchronization by directing the scaling factor. The feasibility of the control is illustrated on a generalized Hénon map and a second-order map. We also show that the control scheme is robust in presence of noise.

MSC:

37M10 Time series analysis of dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
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[1] Pecora, L. M.; Carroll, T. L., Phys. Rev. Lett., 64, 821 (1990)
[2] Yang, X. S.; Chen, G., Chaos Solitons Fractals, 13, 1303 (2002)
[3] Itoh, M.; Murakami, H., IEICE Trans. Fundamentals, E78-A, 285 (1995)
[4] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., IEEE Trans. Circuits Systems I, 44, 874 (1997)
[5] Cao, L. Y.; Lai, Y. C., Phys. Rev. E, 58, 382 (1998)
[6] Mainieri, R.; Rehacek, J., Phys. Rev. Lett., 82, 3042 (1999)
[7] Xu, D., Phys. Rev. E, 63, 27201 (2001)
[8] Xu, D.; Li, Z.; Bishop, S. R., Chaos, 11, 439 (2001)
[9] Xu, D.; Chee, C. Y., Phys. Rev. E, 66, 046218 (2002)
[10] Xu, D.; Chee, C. Y.; Li, C., Chaos Solitons Fractals, 22, 175 (2004)
[11] Chee, C. Y.; Xu, D., Phys. Lett. A, 318, 112 (2003)
[12] Chen, G.; Dong, X., From Chaos to Order: Methodologies, Perspectives, and Applications (1998), World Scientific: World Scientific Singapore
[13] Grassi, G.; Miller, D. A., IEEE Trans. Circuits Systems I, 49, 373 (2002)
[14] Guckenheimer, J.; Holmes, P. J., Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields (1983), Springer-Verlag: Springer-Verlag New York
[15] Rodriguez-Vasquez, A.; Huertas, J. L.; Rueda, A.; Perez-Verdu, B.; Chua, L. O., Proc. IEEE, 75, 1090 (1987)
[16] Konishi, K.; Kokame, H., Phys. Lett. A, 248, 359 (1998)
[17] Itoh, M.; Murakami, H., IEICE Trans. Fundamentals, E77-A, 2092 (1994)
[18] Grassi, G.; Mascolo, S., IEEE Trans. Circuits Systems I, 44, 1011 (1997)
[19] Fortmann, T. E.; Hitz, K. L., An Introduction to Linear Control Systems (1977), Marcel Dekker: Marcel Dekker New York · Zbl 0429.93001
[20] De Angeli, X.; Genesio, R.; Tesi, A., IEEE Trans. Circuits Systems I, 42, 54 (1995)
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