×

Synchronization of an uncertain unified chaotic system via adaptive control. (English) Zbl 1005.93020

The authors are deeply involved in the study of chaotic systems. In the present paper they develop a new approach combining both parameters identification (initial and master-slave) and chaos synchronization, which works for a large class of uncertain chaotic systems. The main idea of the paper is to force the response of the slave system to synchronize with the master system, where the slave system receives driving signals from the master system, for uncertain chaotic systems.

MSC:

93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C40 Adaptive control/observation systems
93A13 Hierarchical systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Chen, G.; Dong, X., From chaos to order: methodologies, perspectives and applications, (1998), World Scientific Singapore
[2] Lü, J.; Lu, J.; Chen, S., Chaotic time series analysis and its application, (2002), Wuhan University Press China
[3] Yu, X.; Song, Y., Chaos synchronization via controlling partial state of chaotic systems, Int. J. bifurcation and chaos, 11, 1737-1741, (2001)
[4] Pecora, L.M.; Carroll, T.L., Synchronization in chaotic systems, Phys. rev. lett., 64, 821-824, (1990) · Zbl 0938.37019
[5] Wang, C.; Ge, S.S., Adaptive synchronization of uncertain chaotic systems via backstepping design, Chaos, solitons and fractals, 12, 1199-1206, (2001) · Zbl 1015.37052
[6] Lü, J.; Zhang, S., Controlling Chen’s chaotic attractor using backstepping design based on parameters identification, Phys. lett. A, 286, 145-149, (2001)
[7] Yang, T.; Yang, L.B.; Yang, C.M., Impulsive control of Lorenz system, Physica D, 110, 18-24, (1997) · Zbl 0925.93414
[8] Fradkov, A.L.; Pogromsky, A.Y., Introduction to control of oscillations and chaos, (1998), World Scientific Singapore · Zbl 0945.93003
[9] Chen, G.; Ueta, T., Yet another chaotic attractor, Int. J. bifurcation and chaos, 9, 1465-1466, (1999) · Zbl 0962.37013
[10] Ueta, T.; Chen, G., Bifurcation analysis of Chen’s attractor, Int. J. bifurcation and chaos, 10, 1917-1931, (2000) · Zbl 1090.37531
[11] Vanĕc̆ek, A.; C̆elikovský, S., Control systems: from linear analysis to synthesis of chaos, (1996), Prentice-Hall London · Zbl 0874.93006
[12] Lü, J.; Chen, G.; Zhang, S., A new chaotic attractor coined, Int. J. bifurcation and chaos, 12, (2002), [to appear] · Zbl 1063.34510
[13] Lü, J.; Chen, G.; Zhang, S., Dynamical analysis of a new chaotic attractor, Int. J. bifurcation and chaos, 12, (2002), [to appear] · Zbl 1044.37021
[14] Lü, J.; Chen, G.; Zhang, S.; Celikovsky, S., Bridge the gap between the Lorenz system and the Chen system, Int. J. bifurcation and chaos, 12, (2002), [to appear] · Zbl 1043.37026
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.