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Adaptive synchronization between two different chaotic dynamical systems. (English) Zbl 1115.37030
Summary: This work presents the synchronization between two different chaotic systems by using an adaptive feedback control scheme. The adaptive synchronization problem between an electrostatic system and electromechanical transducer is investigated. An adaptive linear feedback law with two controllers is proposed to ensure the global chaos synchronization of the nonlinear electrostatic and electromechanical systems. Numerical simulations results are presented to demonstrate the effectiveness of the proposed method.

MSC:
37D45Strange attractors, chaotic dynamics
93D21Adaptive or robust stabilization
93B52Feedback control
78A30Electro- and magnetostatics
37N20Dynamical systems in other branches of physics
93D05Lyapunov and other classical stabilities of control systems
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References:
[1] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems. Phys rev lett 64, 821824 (1990) · Zbl 0938.37019
[2] Chen, G.; Dong, X.: From chaos to order. (1998) · Zbl 0908.93005
[3] Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos. Phys rev lett 64, 1196-1199 (1990) · Zbl 0964.37501
[4] Park, J. H.; Kwon, O. M.: A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos, solitons & fractals 23, 495-501 (2005) · Zbl 1061.93507
[5] Chua, L. O.; Itoh, M.; Kocarev, L.; Eckert, K.: Chaos synchronization in Chua’s circuits. J circuit syst comput 3, 93-108 (1993) · Zbl 0875.94133
[6] Chen, M.; Han, Z.: Controlling and synchronizing chaotic Genesio system via nonlinear feedback control. Chaos, solitons & fractals 17, 709-716 (2003) · Zbl 1044.93026
[7] Lü, J.; Chen, G.; Cheng, D.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system. Int J bifur chaos 12, 2917-2926 (2002) · Zbl 1043.37026
[8] Lu, J.; Wu, X.; Lü, J.: Synchronization of a unified chaotic system and the application in secure communication. Phys lett A 305, 365-370 (2002) · Zbl 1005.37012
[9] Bowong, S.; Kakmeni, F. M. Moukam: Synchronization of uncertain chaotic systems via backstepping approach. Chaos, solitons & fractals 21, 999-1011 (2004) · Zbl 1045.37011
[10] Li, D.; Lu, J. A.; Wu, X.: Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems. Chaos, solitons & fractals 23, 79-85 (2005) · Zbl 1063.37030
[11] Lü, J.; Zhou, T.; Zhang, S.: Chaos synchronization between linearly coupled chaotic systems. Chaos, solitons & fractals 14, 529-541 (2002) · Zbl 1067.37043
[12] Agiza, H. N.; Yassen, M. T.: Synchronization of Rössler and Chen dynamical systems using active control. Phys lett A 278, 191-197 (2001) · Zbl 0972.37019
[13] Park, J. H.: Stability criterion for synchronization of linearly coupled unified chaotic systems. Chaos, solitons & fractals 23, 1319-1325 (2005) · Zbl 1080.37035
[14] Chen, H. K.: Global chaos synchronization of new chaotic systems via nonlinear control. Chaos, solitons & fractals 23, 1245-1251 (2005) · Zbl 1102.37302
[15] Wang, Y.; Guan, Z. H.; Wang, H. O.: Feedback an adaptive control for the synchronization of Chen system via a single variable. Phys lett A 312, 34-40 (2003) · Zbl 1024.37053
[16] Park, J. H.: On synchronization of unified chaotic systems via nonlinear control. Chaos, solitons & fractals 25, 699-704 (2005) · Zbl 1125.93469
[17] Lu, J.; Wu, X.; Han, X.; Lü, J.: Adaptive feedback synchronization of a unified chaotic system. Phys lett A 329, 327-333 (2004) · Zbl 1209.93119
[18] Han, X.; Lu, J. A.; Wu, X.: Adaptive feedback synchronization of Lü systems. Chaos, solitons & fractals 22, 217-221 (2004) · Zbl 1060.93524
[19] Elabbasy, E. M.; Agiza, H. N.; El-Dessoky, M. M.: Adaptive synchronization of Lü system with uncertain parameters. Chaos, solitons & fractals 21, 657-667 (2004) · Zbl 1062.34039
[20] Park, J. H.: Adaptive synchronization of a unified chaotic systems with an uncertain parameter. Int J nonlinear sci numer simulat 6, 201-206 (2005)
[21] Genesio, R.; Tesi, A.: A harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28, 531-548 (1992) · Zbl 0765.93030
[22] Ho, M. C.; Hung, Y. C.: Synchronization of two different systems by using generalized active control. Phys lett A 301, 424-428 (2002) · Zbl 0997.93081
[23] Yassen, M. T.: Chaos synchronization between two different chaotic systems using active control. Chaos, solitons & fractals 23, 131-140 (2005) · Zbl 1091.93520
[24] Fotsin, H.; Bowong, S.; Daafouz, J.: Adaptive synchronization of two chaotic systems consisting of modified van der Pol-Duffing and Chua oscillators. Chaos, solitons & fractals 26, 215-229 (2005) · Zbl 1122.93069
[25] Bowong, S.; Kakmeni, F. M. Moukam: Stability and duration time of chaos synchronization of a class of nonidentical oscillators. Phys scripta 68, 326-332 (2003) · Zbl 1063.70021
[26] Woafo, P.: Transitions to chaos and synchronization in a nonlinear emitter-receiver system. Phys lett A 267, 31-39 (2000)
[27] Yamapi, R.; Orou, J. B. Chabi; Woafo, P.: Harmonic oscillations, stability and chaos control in a non-linear electromechanical system. J sound vibr 259, No. 5, 1253-1264 (2003) · Zbl 1237.34070
[28] Khalil, H. K.: Nonlinear systems. (1995) · Zbl 0925.93461