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Adaptive control and synchronization of a coupled dynamo system with uncertain parameters. (English) Zbl 1142.93422

Summary: This paper treats the adaptive control and synchronization of the coupled dynamo system with unknown parameters. Based on the Lyapunov stability technique, an adaptive control laws are derived such that the coupled dynamo system is asymptotically stable and the two identical dynamo systems are asymptotically synchronized. Also the update rules of the unknown parameters are derived. Finally, numerical simulation of the controlled and synchronized systems are presented.

MSC:

93D21 Adaptive or robust stabilization
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[2] Chen, G.; Dong, X., From chaos to order: methodologies, perspectives and applications (1998), World Scientific: World Scientific Singapore
[3] Wang, Y.; Guan, Z.-H.; Wang, H. O., Feedback and adaptive control for the synchronization of Chen system via a single variable, Phys Lett A, 312, 34-40 (2003) · Zbl 1024.37053
[4] Chen G. Control and synchronization of chaos, a bibliography. Dept Elect Eng Univ Houston, TX, 1997.; Chen G. Control and synchronization of chaos, a bibliography. Dept Elect Eng Univ Houston, TX, 1997.
[5] Carroll, T. L.; Pecora, L. M., Synchronizing chaotic circuits, IEEE Trans Circ Syst I, 38, 453-456 (1991)
[6] Ott, E.; Grebogi, C.; Yorke, J. A., Controlling chaos, Phys Rev Lett, 64, 11, 1196-1199 (1990) · Zbl 0964.37501
[7] Stoten, D. P.; Di Bernardo, M., Application of the minimal control synthesis algorithm to the control synchronization of chaotic systems, Int J Control, 65, 6, 925-938 (1996) · Zbl 0867.93073
[8] Thompson, J.; Stewart, H., Nonlinear dynamics and chaos: geometrical methods for engineers and scientists (1986), John Wiley and Sons: John Wiley and Sons New York · Zbl 0601.58001
[9] Bai, E.-W.; Lonngren, K. E., Synchronization of two Lorenz systems using active control, Chaos, Solitons & Fractals, 8, 1, 51-56 (1997) · Zbl 1079.37515
[10] Ho, M.-C.; Hung, Y.-C., Synchronization of two different systems by using generalized active control, Phys Lett A, 301, 424 (2002) · Zbl 0997.93081
[11] Huang, L.; Feng, R.; Wang, M., synchronization of chaotic system via nonlinear control, Phys Lett A, 320, 271 (2004) · Zbl 1065.93028
[12] Yan, J.; Li, C., On synchronization of three chaotic systems, Chaos, Solitons & Fractals, 23, 5, 1683-1688 (2005) · Zbl 1068.94535
[13] Chen, H.-K., Global chaos synchronization of new chaotic systems via nonlinear control, Chaos, Solitons & Fractals, 23, 4, 1245-1251 (2005) · Zbl 1102.37302
[14] Xie, Q.; Chen, G., Synchronization stability analysis of the chaotic Rossler system, Int J Bifurc Chaos, 6, 11, 2153-2161 (1996) · Zbl 1298.34096
[15] Pecora, L. M.; Carroll, T. L., Deriving systems with chaotic signals, Phys Rev A, 44, 2374-2383 (1991)
[16] El-Gohary, A.; Bukhari, F., Optimal control of Lorenz system during different time intervals, Appl Math Comput, 144, 2-3, 337-351 (2003) · Zbl 1036.49028
[17] El-Gohary, A., Optimal synchronization of Rössler system with complete uncertain parameters, Chaos, Solitons & Fractals, 27, 2, 345-355 (2006) · Zbl 1091.93025
[18] Vanek, A.; Celikovsky, S., Control system: from linear analysis to synthesis to synthesis of chaos (1996), Prentice-Hall: Prentice-Hall London
[19] Cook, P. A., Nonlinear dynamical system (1986), Prentice-Hall: Prentice-Hall London · Zbl 0588.93001
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