×

zbMATH — the first resource for mathematics

A novel active pinning control for synchronization and anti-synchronization of new uncertain unified chaotic systems. (English) Zbl 1209.93071
Summary: This paper discusses the synchronization and anti-synchronization of new Uncertain Unified Chaotic Systems (UUCS). Based on the idea of active control, a novel active pinning control strategy is presented, which only needs a state of new UUCS. The proposed controller can achieve synchronization between a response system and a drive system, and ensure the synchronized robust stability of new UUCS. Numerical simulations of new UUCS show that the controller can make that chaotic systems achieve synchronization or anti-synchronization in a quite short period and both are of good robust stability.

MSC:
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
93D09 Robust stability
93D15 Stabilization of systems by feedback
34H10 Chaos control for problems involving ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lorenz, E.N.: Deterministic non-periodic flows. J. Atmos. Sci. 20, 130–141 (1963) · Zbl 1417.37129
[2] Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64(2), 821–824 (1990) · Zbl 0964.37501
[3] Pecora, L., Carroll, T.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(2), 821–824 (1990) · Zbl 0938.37019
[4] Chen, S., Wang, F., Wang, C.: Synchronizing strict-feedback and general strict-feedback chaotic systems via a single controller. Chaos Solitons Fractals 20(2), 235–243 (2004) · Zbl 1052.37061
[5] Chen, M., Han, Z.: Controlling and synchronizing chaotic Genesio system via nonlinear feedback control. Chaos Solitons Fractals 17(4), 709–716 (2003) · Zbl 1044.93026
[6] Wang, Y., Guan, Z., Wen, X.: Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos Solitons Fractals 19(4), 899–903 (2004) · Zbl 1053.37528
[7] Li, C., Liao, X., Zhang, X.: Impulsive synchronization of chaotic systems. Chaos 15, 023104 (2005). doi: 10.1063/1.1899823 · Zbl 1080.37034
[8] Li, G.: Generalized projective synchronization of two chaotic systems by using active control. Chaos Solitons Fractals 30(1), 77–82 (2006) · Zbl 1144.37372
[9] Li, G., Zhou, S., Yang, K.: Generalized projective synchronization between two different chaotic systems using active backstepping control. Phys. Lett. A 355(4), 326–330 (2006)
[10] Tan, X., Zhang, J., Yang, Y.: Synchronizing chaotic systems using backstepping design. Chaos Solitons Fractals 16(1), 37–45 (2003) · Zbl 1035.34025
[11] Chen, S., Yang, Q., Wang, C.: Impulsive control and synchronization of unified chaotic system. Chaos Solitons Fractals 20(4), 751–758 (2004) · Zbl 1050.93051
[12] Chen, M., Han, Z.: Controlling and synchronizing chaotic Genesio system via nonlinear feedback control. Chaos Solitons Fractals 17(4), 709–716 (2003) · Zbl 1044.93026
[13] Yu, W., Chen, G., Lü, J.: On pinning synchronization of complex dynamical networks. Automatica 45(2), 429–435 (2009) · Zbl 1158.93308
[14] Vaněček, A., Čelikovský, S.: Control Systems: From Linear Analysis to Synthesis of Chaos. Prentice–Hall, London (1996) · Zbl 0874.93006
[15] Li, Z., Chen, G., Halang, W.A.: Homoclinic and heteroclinic orbits in a modified Lorenz system. Inf. Sci. 165, 235–245 (2004) · Zbl 1057.37019
[16] Lü, J., Zhou, T., Zhang, S.: Controlling the Chen attractor using linear feedback based on parameter identification. Chin. Phys. 11(1), 12–16 (2002)
[17] Feng, J., Xu, C., Tang, J.: Controlling Chen’s chaotic attractor using two different techniques based on parameter identification. Chaos Solitons Fractals 32, 1413–1418 (2007) · Zbl 1129.37317
[18] Wang, X., Chen, G.: Pinning control of scale-free dynamical networks. Physica A 310, 521–531 (2002) · Zbl 0995.90008
[19] Li, X., Wang, X., Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circ. Syst. I–Regul. Pap. 51, 2074–2087 (2004) · Zbl 1374.94915
[20] Chen, T., Liu, X., Lu, W.: Pinning complex networks by a single controller. IEEE Trans. Circ. Syst. I—-Regul. Pap. 54, 1317–1326 (2007) · Zbl 1374.93297
[21] Sorrentino, F., di Bernardo, M., Garofalo, F., Chen, G.: Controllability of complex networks via pinning. Phys. Rev. E 75, 046103 (2007) · Zbl 1144.82352
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.