Park, Ju H. Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. (English) Zbl 1137.93035 J. Comput. Appl. Math. 213, No. 1, 288-293 (2008). 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. Cited in 41 Documents MSC: 93C40 Adaptive control/observation systems 93C10 Nonlinear systems in control theory 93C41 Control/observation systems with incomplete information 93C15 Control/observation systems governed by ordinary differential equations Keywords:modified projective synchronization; adaptive control; chaotic systems; Lyapunov method PDF BibTeX XML Cite \textit{J. H. Park}, J. Comput. Appl. Math. 213, No. 1, 288--293 (2008; Zbl 1137.93035) Full Text: DOI 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 [2] Chen, G.; Dong, X., From Chaos to Order (1998), World Scientific: World Scientific Singapore [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 [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 [5] Han, X.; Lu, J. A.; Wu, X., Adaptive feedback synchronization of Lü systems, Chaos, Solitons, Fractals, 22, 221-227 (2004) · Zbl 1060.93524 [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 [9] Lu, J. H.; Lu, J. A., Controlling uncertain Lü system using linear feedback, Chaos, Solitons, Fractals, 17, 127-133 (2003) · Zbl 1039.37019 [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 [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] Ott, E.; Grebogi, C.; Yorke, J. A., Controlling chaos, Phys. Rev. Lett., 64, 1196-1199 (1990) · Zbl 0964.37501 [13] Park, J. H., Adaptive synchronization of a unified chaotic systems with an uncertain parameter, Internat. J. Nonlinear Sci. Numer. Simulation, 6, 2, 201-206 (2005) · Zbl 1401.93123 [14] Park, J. H., Stability criterion for synchronization of linearly coupled unified chaotic systems, Chaos, Solitons, Fractals, 23, 1319-1325 (2005) · Zbl 1080.37035 [15] Park, J. H., On synchronization of unified chaotic systems via nonlinear control, Chaos, Solitons, Fractals, 25, 3, 699-704 (2005) · Zbl 1125.93469 [16] Park, J. H., Adaptive synchronization of a four-dimensional chaotic system with uncertain parameters, Internat. J. Nonlinear Sci. Numer. Simulation, 6, 3, 305-310 (2005) · Zbl 1401.93124 [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 [18] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019 [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 [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 [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 [23] Wu, X.; Lu, J., Parameter identification and backstepping control of uncertain Lü system, Chaos, Solitons, Fractals, 18, 721-729 (2003) · Zbl 1068.93019 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.