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Li, H. Y.; Hu, Y. A.

Robust sliding-mode backstepping design for synchronization control of cross-strict feedback hyperchaotic systems with unmatched uncertainties. (English) Zbl 1219.93026

Commun. Nonlinear Sci. Numer. Simul. 16, No. 10, 3904-3913 (2011).
Summary: This paper is concerned with the synchronization problem for a class of hyperchaotic chaotic systems. Using sliding mode control approach and backstepping control, a robust control scheme is proposed to make most of the synchronization errors of the systems to zero for matched and unmatched uncertainties. And only one of the synchronization errors of the systems may not be zero, but it is bounded. Meanwhile, the chattering phenomenon is eliminated. The proposed methods can be applied to a variety of chaos systems which can be described by the so-called cross-strict feedback form. Numerical simulations are given to demonstrate the efficiency of the proposed control schemes.

Cited in 15 Documents

MSC:

93B12 Variable structure systems
93B35 Sensitivity (robustness)
34H10 Chaos control for problems involving ordinary differential equations
93C73 Perturbations in control/observation systems

Keywords:

hyper-chaos synchronization; cross-strict feedback system; backstepping; sliding mode
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\textit{H. Y. Li} and \textit{Y. A. Hu}, Commun. Nonlinear Sci. Numer. Simul. 16, No. 10, 3904--3913 (2011; Zbl 1219.93026)
Full Text: DOI

References:

[1] Wu, T.; Chen, M. S., Chaos control of the modified Chua’s circuit system, Physica D, 164, 53-58 (2002) · Zbl 1008.37017
[2] Harb, A.; Abedl-Jabbar, N., Controlling Hopf bifurcation and chaos in a small power system, Chaos Solitons Fract, 18, 1055-1063 (2003) · Zbl 1074.93522
[3] Chen, G., Controlling chaos and bifurcations in engineering systems (1999), CRC Press
[4] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-824 (1990) · Zbl 0938.37019
[5] Zhu, C. X., Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters, Appl Math Comput, 215, 557-561 (2009) · Zbl 1182.37028
[6] Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D. L.; Zhou, C. S., The synchronization of chaotic systems, Phys Rep, 366, 1-101 (2002) · Zbl 0995.37022
[7] Yan, Z., Controlling hyperchaos in the new hyperchaotic Chen system, Appl Math Comput, 168, 1239-1250 (2005) · Zbl 1160.93384
[8] Wang, F.; Liu, C., A new criterion for chaos and hyperchaos synchronization using linear feedback control, Phys Lett A, 360, 274-278 (2006) · Zbl 1236.93131
[9] Wu, X. Y.; Zhang, H. M., Synchronization of two hyperchaotic systems via adaptive control, Chaos Solitons Fract, 39, 2268-2273 (2009) · Zbl 1197.37046
[10] Jia, Q., Adaptive control and synchronization of a new hyperchaotic system with unknown parameters, Phys Lett A, 362, 424-429 (2007) · Zbl 1197.34107
[11] Zhou, X. B.; Wu, Y.; Li, Y.; Xue, H. Q., Adaptive control and synchronization of a new modified hyperchaotic Lu system with uncertain parameters Chaos, Chaos Solitons Fract, 39, 2477-2483 (2009) · Zbl 1197.37052
[12] Wang, J.; Gao, J. F.; Ma, X. K., Synchronization control of cross-strict feedback hyperchaotic system based on cross active backstepping design, Phys Lett A, 369, 452-457 (2007)
[13] Zhang, H.; Ma, X. K.; Li, M.; Zou, J. L., Controlling and tracking hyperchaotic Rossler system via active backstepping design, Chaos Solitons Fract, 26, 353-361 (2005) · Zbl 1153.93381
[14] Yu, Y. G.; Zhang, S. C., Adaptive backstepping synchronization of uncertain chaotic system Chaos, Chaos Solitons Fract, 21, 643-649 (2004) · Zbl 1062.34053
[15] Tan, X. H.; Zhang, J. Y.; Yang, Y. R., Synchronizing chaotic systems using backstepping design, Chaos Solitons Fract, 16, 37-45 (2003) · Zbl 1035.34025
[16] WANG, C.; GE, S. S., Synchronization of two uncertain chaotic systems via adaptive backstepping, Int J Bifur Chaos, 11, 1743-1751 (2001)
[17] Bowong, S.; Kakmeni, F. M.M., Synchronization of uncertain chaotic systems via backstepping approach, Chaos Solitons Fract, 21, 999-1011 (2004) · Zbl 1045.37011
[18] Kittel, A.; Parisi, J.; Pyragas, K., Delayed feedback control of chaos by self-adapted delay time, Phys Lett A, 198, 433-436 (1995)
[19] Chen, F. X.; Wang, W.; Chen, L.; Zhang, W. D., Adaptive chaos synchronization based on LMI technique, Phys Scr, 75, 285-288 (2007)
[20] Haeri, M.; Emadzadeh, A. A., Synchronizing different chaotic systems using active sliding mode control, Chaos Solitons Fract, 31, 119-129 (2007) · Zbl 1142.93394
[21] Yan, J. J.; Hung, M. L.; Chiang, T. Y.; Yang, Y. S., Robust synchronization of chaotic systems via adaptive sliding mode control, Phys Lett A, 356, 220-225 (2006) · Zbl 1160.37352
[22] Roopaei, M.; Sahraei, B. R.; Lin, T. C., Adaptive sliding mode control in a novel class of chaotic systems, Commun Nonlinear Sci Numer Simul, 15, 4158-4170 (2010) · Zbl 1222.93124
[23] Yau, H. T., Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control, Mech Syst Signal Process, 22, 408-418 (2008)
[24] Wang, H.; Han, Z. Z.; Xie, Q. Y.; Zhang, W., Finite-time chaos control via nonsingular terminal sliding mode control, Commun Nonlinear Sci Numer Simul, 14, 2728-2733 (2009) · Zbl 1221.37225
[25] Huang, C. F.; Cheng, K. H.; Yan, J. J., Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties, Commun Nonlinear Sci Numer Simul, 14, 2784-2792 (2009)
[26] Xiang, W.; Huangpu, Y. G., Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties, Commun Nonlinear Sci Numer Simul, 15, 3241-3247 (2010) · Zbl 1222.93045
[27] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P., Nonlinear and adaptive control design (1995), Wiley · Zbl 0763.93043
[28] Park, J. H., Synchronization of Genesio chaotic system via backstepping approach, Chaos Solitons Fract, 27, 1369-1375 (2006) · Zbl 1091.93028
[29] Li, G. H.; Zhou, S. P.; Yang, K., Generalized projective synchronization between two different chaotic systems using active backstepping control, Phys Lett A, 355, 326-330 (2006)
[30] Li, Y.; Tang, W. K.S.; Chen, G. R., Generating hyperchaos via state feedback control, Int J Bifur Chaos, 15, 3367-3375 (2005)
[31] Wu, X. Y.; Guan, Z. H.; Wu, Z. P., Adaptive synchronization between two different hyperchaotic systems, Nonlinear Anal, 68, 1346-1351 (2008) · Zbl 1151.34041
[32] Sun, Y. J.; Lien, C. H.; Hsieh, J. G., Global exponential stabilization for a class of uncertain nonlinear systems with control constraint, IEEE Trans Automat Contr, 43, 674-677 (1998) · Zbl 0912.93055
[33] Ma, J.; Zhang, A. H.; Xia, Y. F.; Zhang, L. P., Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems, Appl Math Comput, 215, 3318-3326 (2010) · Zbl 1181.93032
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