×

zbMATH — the first resource for mathematics

Adaptive synchronization of uncertain unified chaotic systems via novel feedback controls. (English) Zbl 1347.93137
Summary: This paper is concerned with the robust adaptive synchronization problem for unified chaotic systems with parameter variation, system uncertainties, and external disturbances. By combining adaptive method and positive time-varying integral functions, novel adaptive synchronization schemes are proposed. It is shown that the synchronization errors between the drive and response chaotic systems converge to zero asymptotically. Finally, illustrative examples about Lorenz chaotic system, Chen chaotic system, and Lü chaotic system are provided to demonstrate the effectiveness and applicability of the proposed design method.

MSC:
93B52 Feedback control
34D06 Synchronization of solutions to ordinary differential equations
93C40 Adaptive control/observation systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C73 Perturbations in control/observation systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Wei, GW; Meng, Z; Lai, CH, Tailoring wavelets for chaos control, Phys. Rev. Lett., 89, 284103, (2002)
[2] Boccaletti, S; Grebogi, C; Lai, YC; Mancini, H; Maza, D, The control of chaos: theory and applications, Phys. Rep., 329, 103-197, (2000)
[3] Boccaletti, S; Kurths, J; Osipov, G; Valladares, DL; Zhou, CS, The synchronization of chaotic systems, Phys. Rep., 366, 1-101, (2002) · Zbl 0995.37022
[4] Park, JH, Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter, Chaos Solitons Fractals, 34, 1552-1559, (2007) · Zbl 1152.93407
[5] Park, JH; Ji, DH; Won, SC; Lee, SM, Adaptive \({\cal{H}}_{∞ }\) synchronization of unified chaotic systems, Mod. Phys. Lett. B, 23, 1157-1169, (2009) · Zbl 1179.37123
[6] Zhang, Z; Wang, Y; Du, Z, Adaptive synchronization of single-degree-of-freedom oscillators with unknown parameters, Appl. Math. Comput., 218, 6833-6840, (2012) · Zbl 1254.34082
[7] Ye, D; Zhao, X, Robust adaptive synchronization for a class of chaotic systems with actuator failures and nonlinear uncertainty, Nonlinear Dyn., 76, 973-983, (2014) · Zbl 1306.93062
[8] Yan, JJ; Hung, ML; Liao, TL, Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters, J. Sound Vib., 298, 298-306, (2006) · Zbl 1243.93097
[9] Zhang, R; Yang, S, Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach, Nonlinear Dyn., 71, 269-278, (2013)
[10] Yang, C.C., Lin, C.L.: Adaptive sliding mode control for chaotic synchronization of oscillator with input nonlinearity. J. Vib. Control (2013). doi:10.1177/1077546313487243
[11] Wang, C; Ge, SS, Synchronization of two uncertain chaotic systems via adaptive backstepping, Int. J. Bifurc. Chaos, 11, 1743-1751, (2001)
[12] Park, JH, Synchronization of Genesio chaotic system via backstepping approach, Chaos Solitons Fractals, 27, 1369-1375, (2006) · Zbl 1091.93028
[13] Wang, J; Gao, JF; Ma, XK; Liang, ZH, A general response system control method based on backstepping design for synchronization of continuous scalar chaotic signal, Chin. Phys. Lett., 23, 2027-2029, (2006)
[14] Hu, YA; Li, HY; Huang, H, Prescribed performance-based backstepping design for synchronization of cross-strict feedback hyperchaotic systems with uncertainties, Nonlinear Dyn., 76, 103-113, (2014) · Zbl 1319.34117
[15] Sun, J; Zhang, Y, Impulsive control and synchronization of chua’s oscillators, Math. Comput. Simul., 66, 499-508, (2004) · Zbl 1113.93088
[16] Liu, D; Wu, Z; Ye, Q, Adaptive impulsive synchronization of uncertain drive-response complex-variable chaotic systems, Nonlinear Dyn., 75, 209-216, (2014) · Zbl 1281.34089
[17] Chen, CS, Optimal nonlinear observers for chaotic synchronization with message embedded, Nonlinear Dyn., 61, 623-632, (2010) · Zbl 1204.94058
[18] Zhang, Z; Shao, H; Wang, Z; Shen, H, Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems, Appl. Math. Comput., 218, 7614-7621, (2012) · Zbl 1250.34045
[19] Yan, JJ; Hung, ML; Chiang, TY; Yang, YS, Robust synchronization of chaotic systems via adaptive sliding mode control, Phys. Lett. A, 356, 220-225, (2006) · Zbl 1160.37352
[20] Sun, YJ, A novel chaos synchronization of uncertain mechanical systems with parameter mismatchings, external excitations, and chaotic vibrations, Commun. Nonlinear Sci. Numer. Simul., 17, 496-504, (2012) · Zbl 1239.93051
[21] Yang, CC, Synchronizations of rotating pendulums via self-learning terminal sliding-mode control subject to input nonlinearity, Nonlinear Dyn., 72, 695-705, (2013)
[22] Zhang, Z; Lu, J; Gao, L; Shao, H, Exponential synchronization of Genesio-Tesi chaotic systems with partially known uncertainties and completely unknown dead-zone nonlinearity, J. Frankl. Inst., 350, 347-357, (2013) · Zbl 1278.93119
[23] Koofigar, HR; Hosseinnia, S; Sheikholeslam, F, Robust adaptive synchronization of uncertain unified chaotic systems, Nonlinear Dyn., 59, 477-483, (2010) · Zbl 1183.70072
[24] Koofigar, HR; Sheikholeslam, F; Hosseinnia, S, Robust adaptive synchronization for a general class of uncertain chaotic systems with application to chua’s circuit, Chaos, 21, 043134, (2011) · Zbl 1317.34087
[25] Koofigar, HR; Hosseinnia, S; Sheikholeslam, F, Robust adaptive nonlinear control for uncertain control-affine systems and its applications, Nonlinear Dyn., 56, 13-22, (2009) · Zbl 1170.93331
[26] Koofigar, HR; Hosseinnia, S; Sheikholeslam, F, Robust adaptive control of nonlinear systems with time-varying parameters and its application to chua’s circuit, IEICE Trans. Fundam., E91-A, 2507-2513, (2008)
[27] Cao, Y.Y., Sun, Y.X., Lam, J.: Delay dependent robust \({\cal{H}}_{∞ }\) control for uncertain systems with time varying delays. IEE Proc. Control Theory Appl. 143(3), 338-344 (1998)
[28] Polycarpous, M.M.: Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Autom. Control 41(3), 447-451 (1996)
[29] Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall, Upper Saddle River (1996) · Zbl 0839.93002
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.