×

Review article on adaptive synchronization of chaotic systems with unknown parameters. (English) Zbl 1235.93180

Summary: This review article studies some adaptive chaos synchronization methods that were already presented in the literature for a general class of chaotic systems. In this regard, the proposed adaptive controllers and parameter update laws in several papers are inspected, and it is shown that many works suffer from novelty and they can be categorized in a union set.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI

References:

[1] Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990) · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821
[2] Heagy, J.F., Carroll, T.L., Pecora, L.M.: Synchronous chaos in coupled oscillator systems. Phys. Rev. E 50, 1874–1885 (1994) · doi:10.1103/PhysRevE.50.1874
[3] Almeida, D.I.R., Alvarez, J.: Robust synchronization of nonlinear SISO systems using sliding mode control. Nonlinear Dyn. 46, 293–306 (2006) · Zbl 1170.70385 · doi:10.1007/s11071-006-9043-y
[4] Roopaei, M., Jahromi, M.Z., John, R., Lin, T.-C.: Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input. Commun. Nonlinear Sci. Numer. Simul. 15, 2536–2545 (2010) · Zbl 1222.93123 · doi:10.1016/j.cnsns.2009.09.022
[5] Bowong, S.: Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach. Nonlinear Dyn. 49, 59–70 (2007) · Zbl 1181.70043 · doi:10.1007/s11071-006-9103-3
[6] Zhang, J., Tang, W.: Control and synchronization for a class of new chaotic systems via linear feedback. Nonlinear Dyn. 58, 675–686 (2009) · Zbl 1183.70075 · doi:10.1007/s11071-009-9509-9
[7] Effa, J.Y., Essimbi, B.Z., Ngundam, J.M.: Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control. Nonlinear Dyn. 58, 39–47 (2009) · Zbl 1183.78019 · doi:10.1007/s11071-008-9459-7
[8] Jun, W.X., Sen, L.J., Rong, C.G.: Chaos synchronization of Rikitake chaotic attractor using the passive control technique. Nonlinear Dyn. 53, 45–53 (2008) · Zbl 1170.70403 · doi:10.1007/s11071-007-9294-2
[9] M-Campaña, J.A., C-Toledo, B., Chen, G.: Synchronization of chaotic systems from a fuzzy regulation approach. Fuzzy Sets Syst. 160, 2860–2875 (2009) · Zbl 1176.93047 · doi:10.1016/j.fss.2008.12.006
[10] Kuntanapreeda, S.: Chaos synchronization of unified chaotic systems via LMI. Phys. Lett. A 373, 2837–2840 (2009) · Zbl 1233.93047 · doi:10.1016/j.physleta.2009.06.006
[11] Wang, H., Han, Z.-z., Zhang, W., Xie, Q.-y.: Synchronization of unified chaotic systems with uncertain parameters based on the CLF. Nonlinear Anal. Real World Appl. 10, 715–722 (2009) · Zbl 1167.37332 · doi:10.1016/j.nonrwa.2007.10.025
[12] Huang, J.: Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters. Phys. Lett. A 372, 4799–4804 (2008) · Zbl 1221.93127 · doi:10.1016/j.physleta.2008.05.025
[13] Huang, J.: Chaos synchronization between two novel different hyperchaotic systems with unknown parameters. Nonlinear Anal. Theory Methods Appl. 69, 1–8 (2007)
[14] Yassen, M.T.: Adaptive synchronization of two different uncertain chaotic systems. Phys. Lett. A 337, 335–341 (2005) · Zbl 1136.34314 · doi:10.1016/j.physleta.2005.01.070
[15] Lu, J., Cao, J.: Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. Chaos 15, 1–9 (2005) · Zbl 1144.37378
[16] Chen, X., Lu, J.: Adaptive synchronization of different chaotic systems with fully unknown parameters. Phys. Lett. A 364, 123–128 (2007) · Zbl 1203.93161 · doi:10.1016/j.physleta.2006.11.092
[17] Zhu, C.: Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters. Appl. Math. Comput. 215, 557–561 (2009) · Zbl 1182.37028 · doi:10.1016/j.amc.2009.05.026
[18] Wu, X., Guan, Z.-H., Wu, Z.: Adaptive synchronization between two different hyperchaotic systems. Nonlinear Anal. 68, 1346–1351 (2008) · Zbl 1151.34041 · doi:10.1016/j.na.2006.12.028
[19] Zhou, X., Wu, Y., Li, Y., Xue, H.: Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters. Appl. Math. Comput. 1–6 (2008) · Zbl 1155.37026
[20] Zhang, H., Huang, W., Wang, Z., Chai, T.: Adaptive synchronization between two different chaotic systems with unknown parameters. Phys. Lett. A 350, 363–366 (2006) · Zbl 1195.93121 · doi:10.1016/j.physleta.2005.10.033
[21] Li, S., Xu, W., Li, R.: Synchronization of two different chaotic systems with unknown parameters. Phys. Lett. A 361, 98–102 (2007) · Zbl 1170.37310 · doi:10.1016/j.physleta.2006.09.068
[22] Zhang, G., Liu, Z., Zhang, J.: Adaptive synchronization of a class of continuous chaotic systems with uncertain parameters. Phys. Lett. A 372, 447–450 (2008) · Zbl 1217.37036 · doi:10.1016/j.physleta.2007.07.080
[23] Xu, W., Yang, X.L., Sun, Z.K.: Full- and reduced-order synchronization of a class of time-varying systems containing uncertainties. Nonlinear Dyn. 52, 19–25 (2008) · Zbl 1170.70369 · doi:10.1007/s11071-007-9252-z
[24] Vincent, U.E., Guo, R.: A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 14, 3925–3932 (2009) · Zbl 1221.93134 · doi:10.1016/j.cnsns.2008.09.006
[25] Wang, Z.L., Shi, X.R.: Adaptive Q–S synchronization of non-identical chaotic systems with unknown parameters. Nonlinear Dyn. 59, 559–567 (2010) · Zbl 1189.93075 · doi:10.1007/s11071-009-9562-4
[26] Khalil, H.: Nonlinear Systems, 2nd edn. Prentice Hall, New York (1996) · Zbl 0842.93033
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.