×

Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems. (English) Zbl 1122.93311

Summary: Projective synchronization, characterized by a scaling factor that two coupled systems synchronize proportionally, is usually observable in a class of nonlinear dynamical systems with partial-linearity. We show that, by using an observer-based control, the synchronization could be realized in a general class of chaotic systems regardless of partial-linearity. In addition, this technique overcomes some limitations in previous work, capable to achieve a full-state synchronization with a specified scaling factor, and adjust the scaling factor arbitrarily in due course of control without degrading the controllability. Feasibility of the technique is illustrated for a chaotic circuit converter and the Chen’s attractor.

MSC:

93B05 Controllability
93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Pecora, L. M.; Carrol, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 8, 821-825 (1990)
[2] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., Phase synchronization in driven and coupled chaotic oscillators, IEEE Trans. Circ. Syst. I, 44, 10, 874-881 (1997)
[3] Anishchenko, V. S.; Vadivasova, T. E.; Postnov, D. E.; Safonova, M. A., Synchronization of chaos, Int. J. Bifurcat. Chaos, 2, 633-644 (1992) · Zbl 0876.34039
[4] Kocarev, L.; Parlitz, U., Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems, Phys. Rev. Lett., 76, 11, 1816-1819 (1996)
[5] Mainieri, R.; Rehacek, J., Projective synchronization in three-dimensional chaotic systems, Phys. Rev. Lett., 82, 15, 3042-3045 (1999)
[6] Cao, L. Y.; Lai, Y. C., Antiphase synchronism in chaotic systems, Phys. Rev. E, 58, 1, 382-386 (1998)
[7] Kawata, J.; Nishio, Y.; Dedieu, H.; Ushida, A., Performance comparison of communication systems using chaos synchronization, IEICE Trans. Fund., E82-A, 7, 1322-1328 (1999)
[8] Chee, C. Y.; Xu, D., Secure digital communication using controlled projective synchronisation of chaos, Chaos, Solitons & Fractals, 23, 3, 1063-1070 (2005) · Zbl 1068.94010
[9] Xu, D., Control of projective synchronization in chaotic systems, Phys. Rev. E, 63, 2, 027201 (2001)
[10] Xu, D.; Li, Z.; Bishop, S. R., Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems, Chaos, 11, 3, 439-442 (2001) · Zbl 0996.37075
[11] Xu, D.; Chee, C. Y., Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension, Phys. Rev. E, 66, 4, 046218 (2002)
[12] Rössler, O. E., An equation for hyperchaos, Phys. Lett. A, 71, 2-3, 155-157 (1979) · Zbl 0996.37502
[13] Grassi, G.; Mascolo, S., Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal, IEEE Trans. Circ. Syst. I, 44, 10, 1011-1014 (1997)
[14] Morgül, O.¨; Solak, E., Observer based synchronization of chaotic systems, Phys. Rev. E, 54, 5, 4803 (1996)
[15] Rulkov, N. F., Images of synchronized chaos: experiments with circuits, Chaos, 6, 3, 262-279 (1996)
[16] Zhong, G. Q.; Tang, W. K.S., Circuitry implementation and synchronization of Chen’s attractor, Int. J. Bifurcat. Chaos, 12, 6, 1423-1427 (2002)
[17] Matsumoto, T.; Chua, L. O.; Kobayashi, K., Hyperchaos: laboratory experiment and numerical confirmation, IEEE Trans. Circ. Syst., 33, 11, 1143-1147 (1986)
[18] Chua, L. O., Global unfolding of Chua’s circuit, IEICE Trans. Fund., E76-A, 5, 704-734 (1993)
[19] Tamaševičius, A.; Čenys, A.; Mykolaitis, G.; Namajūnas, A.; Lindberg, E., Hyperchaotic oscillator with gyrators, Electron. Lett., 33, 7, 542-544 (1997)
[20] Fradkov, A. L.; Markov, A. Y., Adaptive synchronization of chaotic systems based on speed gradient method and passification, IEEE Trans. Circ. Syst. I, 44, 10, 905-912 (1997)
[21] Lorenz, E. N., Deterministic nonperiodic flows, J. Atmos. Sci., 20, 130-141 (1963) · Zbl 1417.37129
[22] Paraskevopoulos, P. N., Modern control engineering (2002), Marcel Dekker, Inc: Marcel Dekker, Inc New York · Zbl 0986.93001
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.