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Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. (English) Zbl 1137.93035
Summary: This article is concerned with the modified projective synchronization problem for a class of four-dimensional chaotic system with uncertain parameters. By utilizing Lyapunov method, an adaptive control scheme for the synchronization has been presented. The control performances are verified by a numerical simulation.
MSC:
93C40Adaptive control systems
93C10Nonlinear control systems
93C41Control problems with incomplete information
93C15Control systems governed by ODE
References:
[1]Chen, H. K.: Global chaos synchronization of new chaotic systems via nonlinear control, Chaos, solitons, fractals 23, 1245-1251 (2005) · Zbl 1102.37302 · doi:10.1016/j.chaos.2004.06.040
[2]Chen, G.; Dong, X.: From chaos to order, (1998)
[3]Chen, M.; Han, Z.: Controlling and synchronizing chaotic Genesio system via nonlinear feedback control, Chaos, solitons, fractals 17, 709-716 (2003) · Zbl 1044.93026 · doi:10.1016/S0960-0779(02)00487-3
[4]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 · doi:10.1016/j.chaos.2003.12.028
[5]Han, X.; Lu, J. A.; Wu, X.: Adaptive feedback synchronization of Lü systems, Chaos, solitons, fractals 22, 221-227 (2004) · Zbl 1060.93524 · doi:10.1016/j.chaos.2003.12.103
[6]Hwang, C. C.; Hsieh, J. Y.; Lin, R. S.: A linear continuous feedback control of Chua’s circuit, Chaos, solitons, fractals 8, 1507-1515 (1997)
[7]Li, G. H.: Generalized projective synchronization between Lorenz system and Chen’s system, Chaos, solitons, fractals 32, 1454-1458 (2007) · Zbl 1129.37013 · doi:10.1016/j.chaos.2005.11.073
[8]G.H. Li, Modified projective synchronization of chaotic system, Chaos, Solitons, Fractals, in press, doi: 10.1016/j.chaos.2005.12.009.
[9]Lu, J. H.; Lu, J. A.: Controlling uncertain Lü system using linear feedback, Chaos, solitons, fractals 17, 127-133 (2003) · Zbl 1039.37019 · doi:10.1016/S0960-0779(02)00456-3
[10]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 · doi:10.1016/j.physleta.2004.07.024
[11]Lü, J.; Zhou, T.; Zhang, S.: Chaos synchronization between linearly coupled chaotic systems, Chaos, solitons, fractals 14, 529-541 (2002) · Zbl 1067.37043 · doi:10.1016/S0960-0779(02)00005-X
[12]Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos, Phys. rev. Lett. 64, 1196-1199 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[13]Park, J. H.: Adaptive synchronization of a unified chaotic systems with an uncertain parameter, Internat. J. Nonlinear sci. Numer. simulation 6, No. 2, 201-206 (2005)
[14]Park, J. H.: Stability criterion for synchronization of linearly coupled unified chaotic systems, Chaos, solitons, fractals 23, 1319-1325 (2005) · Zbl 1080.37035 · doi:10.1016/j.chaos.2004.06.029
[15]Park, J. H.: On synchronization of unified chaotic systems via nonlinear control, Chaos, solitons, fractals 25, No. 3, 699-704 (2005) · Zbl 1125.93469 · doi:10.1016/j.chaos.2004.11.031
[16]Park, J. H.: Adaptive synchronization of a four-dimensional chaotic system with uncertain parameters, Internat. J. Nonlinear sci. Numer. simulation 6, No. 3, 305-310 (2005) · Zbl 1093.93537 · doi:10.1016/j.chaos.2005.02.002
[17]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 · doi:10.1016/j.chaos.2004.05.023
[18]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys. rev. Lett. 64, 821-824 (1990)
[19]Qi, G.; Du, S.; Chen, G.; Chen, Z.; Yan, Z.: On a four-dimensional chaotic system, Chaos, solitons, fractals 23, 1671-1682 (2005) · Zbl 1071.37025 · doi:10.1016/j.chaos.2004.06.054
[20]Rulkov, N. F.; Sushchik, M. M.; Tsimring, L. S.; Abarbanel, H. D. I.: Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. rev. E 51, 980-994 (1995)
[21]Wang, Y. W.; Guan, Z. H.: Generalized synchronization of continuous chaotic systems, Chaos, solitons, fractals 27, 97-101 (2006) · Zbl 1083.37515 · doi:10.1016/j.chaos.2004.12.038
[22]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 · doi:10.1016/S0375-9601(03)00573-5
[23]Wu, X.; Lu, J.: Parameter identification and backstepping control of uncertain Lü system, Chaos, solitons, fractals 18, 721-729 (2003) · Zbl 1068.93019 · doi:10.1016/S0960-0779(02)00659-8