Previous |  Up |  Next

Article

Title: Adaptive finite-time synchronization of cross-strict feedback hyperchaotic systems with parameter uncertainties (English)
Author: Li, Hai-Yan
Author: Hu, Yun-An
Author: Wang, Rui-Qi
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 49
Issue: 4
Year: 2013
Pages: 554-567
Summary lang: English
.
Category: math
.
Summary: This paper is concerned with the finite-time synchronization problem for a class of cross-strict feedback underactuated hyperchaotic systems. Using finite-time control and backstepping control approaches, a new robust adaptive synchronization scheme is proposed to make the synchronization errors of the systems with parameter uncertainties zero in a finite time. Appropriate adaptive laws are derived to deal with the unknown parameters of the systems. The proposed method can be applied to a variety of chaotic systems which can be described by the so-called cross-strict feedback systems. Numerical simulations are given to demonstrate the efficiency of the proposed control scheme. (English)
Keyword: finite-time synchronization
Keyword: cross-strict feedback hyperchaotic system
Keyword: backstepping
Keyword: adaptive control
MSC: 34C28
MSC: 34D06
MSC: 34H10
MSC: 34K35
.
Date available: 2013-09-17T16:26:42Z
Last updated: 2013-09-17
Stable URL: http://hdl.handle.net/10338.dmlcz/143445
.
Reference: [1] Aghababa, M. P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique..Appl. Math. Modelling 35 (2011), 3080-3091. Zbl 1219.93023, MR 2776263, 10.1016/j.apm.2010.12.020
Reference: [2] Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., Zhou, C. S.: The synchronization of chaotic systems..Phys. Rep. 366 (2002), 1-101. Zbl 0995.37022, MR 1913567, 10.1016/S0370-1573(02)00137-0
Reference: [3] Bowong, S., Kakmeni, F. M. M.: Synchronization of uncertain chaotic systems via backstepping approach..Chaos Solitons Fractals 21 (2004), 999-1011. Zbl 1045.37011, MR 2042817, 10.1016/j.chaos.2003.12.084
Reference: [4] Chen, F. X., Wang, W., Chen, L., Zhang, W. D.: Adaptive chaos synchronization based on LMI technique..Phys. Scr. 75 (2007), 285-288. 10.1088/0031-8949/75/3/010
Reference: [5] Chen, G.: Controlling Chaos and Bifurcations in Engineering Systems..CRC Press, Boca Raton 1999. Zbl 0929.00012, MR 1756081
Reference: [6] Haeri, M., Emadzadeh, A. A.: Synchronizing different chaotic systems using active sliding mode control..Chaos Solitons Fractals 31 (2007), 119-129. Zbl 1142.93394, MR 2263270, 10.1016/j.chaos.2005.09.037
Reference: [7] Han, J. Q., Wang, W.: Nonlinear tracking differentiator..System Sci. Math. 14 (1994), 177-183. Zbl 0830.93038
Reference: [8] Harb, A., Jabbar, N. A.: Controlling Hopf bifurcation and chaos in a small power system..Chaos Solitons Fractals 18 (2003), 1055-1063. Zbl 1074.93522, 10.1016/S0960-0779(03)00073-0
Reference: [9] Huang, C. F., Cheng, K. H., Yan, J. J.: Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties..Comm. Nonlinear Sci. Numer. Simul. 14 (2009), 2784-2792. 10.1016/j.cnsns.2008.09.017
Reference: [10] Jia, Q.: Adaptive control and synchronization of a new hyperchaotic system with unknown parameters..Phys. Lett. A 362 (2007), 424-429. Zbl 1197.34107, 10.1016/j.physleta.2006.10.044
Reference: [11] Kittel, A., Parisi, J., Pyragas, K.: Delayed feedback control of chaos by self-adapted delay time..Phys. Lett. A 198 (1995), 433-436. 10.1016/0375-9601(95)00094-J
Reference: [12] Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design..Wiley, New York 1995.
Reference: [13] Li, G. H., Zhou, S. P., Yang, K.: Generalized projective synchronization between two different chaotic systems using active backstepping control..Phys. Lett. A 355 (2006), 326-330. 10.1016/j.physleta.2006.02.049
Reference: [14] Li, H. Y., Hu, Y. A.: Robust sliding-mode backstepping design for synchronization control of cross-strict feedback hyperchaotic systems with unmatched uncertainties..Comm. Nonlinear Sci. Numer. Simul. 16 (2011), 3904-3913. Zbl 1219.93026, MR 2802696, 10.1016/j.cnsns.2011.02.031
Reference: [15] Li, H. Y., Hu, Y. A.: Backstepping-Based Synchronization Control of Cross-Strict Feedback Hyper-Chaotic Systems..Chinese Phys. Lett. 28 (2011), 120508.
Reference: [16] Lu, X. Q., Lu, R. Q., Chen, S. H., Lü, J. H.: Finite-time distributed tracking control for multi-agent systems with a virtual leader..IEEE Trans. Circuits Syst. I 60 (2013), 352-362. MR 3017545, 10.1109/TCSI.2012.2215786
Reference: [17] 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 (2010), 3318-3326. Zbl 1181.93032, MR 2576820, 10.1016/j.amc.2009.10.020
Reference: [18] Park, J. H.: Synchronization of Genesio chaotic system via backstepping approach..Chaos Solitons Fractals 27 (2006), 1369-1375. Zbl 1091.93028, MR 2164861, 10.1016/j.chaos.2005.05.001
Reference: [19] Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems..Phys. Rev. Lett. 64 (1990), 821-824. Zbl 1098.37553, MR 1038263, 10.1103/PhysRevLett.64.821
Reference: [20] Pourmahmood, M., Khanmohammadi, S., Alizadeh, G.: Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller..Comm. Nonlinear Sci. Numer. Simul. 16 (2011), 2853-2868. Zbl 1221.93131, MR 2772300, 10.1016/j.cnsns.2010.09.038
Reference: [21] Roopaei, M., Sahraei, B. R., Lin, T. C.: Adaptive sliding mode control in a novel class of chaotic systems..Comm. Nonlinear Sci. Numer. Simul. 15 (2010), 4158-4170. Zbl 1222.93124, MR 2652685, 10.1016/j.cnsns.2010.02.017
Reference: [22] Tan, X. H., Zhang, J. Y., Yang, Y. R.: Synchronizing chaotic systems using backstepping design..Chaos Solitons Fractals 16 (2003), 37-45. Zbl 1035.34025, MR 1941155, 10.1016/S0960-0779(02)00153-4
Reference: [23] Wang, C., Ge, S. S.: Synchronization of two uncertain chaotic systems via adaptive backstepping..Internat. J. Bifur. Chaos 11 (2001), 1743-1751. 10.1142/S0218127401002985
Reference: [24] Wang, F., Liu, C.: A new criterion for chaos and hyperchaos synchronization using linear feedback control..Phys. Lett. A 360 (2006), 274-278. Zbl 1236.93131, 10.1016/j.physleta.2006.08.037
Reference: [25] Wang, H., Han, Z. Z., Xie, Q. Y., Zhang, W.: Finite-time chaos control via nonsingular terminal sliding mode control..Comm. Nonlinear Sci. Numer. Simul. 14 (2009), 2728-2733. Zbl 1221.37225, MR 2483882, 10.1016/j.cnsns.2008.08.013
Reference: [26] Wang, H., Han, Z. Z., Xie, Q. Y., Zhang, W.: Finite-time synchronization of uncertain unified chaotic systems based on CLF..Nonlinear Anal.: Real World Appl. 10 (2009), 2842-2849. Zbl 1183.34072, MR 2523247
Reference: [27] Wang, H., Han, Z. Z., Xie, Q. Y., Zhang, W.: Finite-time chaos synchronization of unified chaotic system with uncertain parameters..Comm. Nonlinear Sci. Numer. Simul. 14 (2009), 2239-2247. 10.1016/j.cnsns.2008.04.015
Reference: [28] 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 (2007), 452-457. 10.1016/j.physleta.2007.05.038
Reference: [29] Wu, T., Chen, M. S.: Chaos control of the modified Chua's circuit system..Physica D 164 (2002), 53-58. Zbl 1008.37017, MR 1910015, 10.1016/S0167-2789(02)00360-3
Reference: [30] Wu, X. Y., Zhang, H. M.: Synchronization of two hyperchaotic systems via adaptive control..Chaos Solitons Fractals 39 (2009), 2268-2273. Zbl 1197.37046, 10.1016/j.chaos.2007.06.100
Reference: [31] Xiang, W., Huangpu, Y. G.: Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties..Comm. Nonlinear Sci. Numer. Simul. 15 (2010), 3241-3247. Zbl 1222.93045, MR 2646151, 10.1016/j.cnsns.2009.12.012
Reference: [32] 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 (2006), 220-225. Zbl 1160.37352, 10.1016/j.physleta.2006.03.047
Reference: [33] Yan, Z.: Controlling hyperchaos in the new hyperchaotic Chen system..Appl. Math. Comput. 168 (2005), 1239-1250. Zbl 1160.93384, MR 2171776, 10.1016/j.amc.2004.10.016
Reference: [34] Yau, H. T.: Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control..Mech. Syst. Signal Process 22 (2008), 408-418. 10.1016/j.ymssp.2007.08.007
Reference: [35] Yu, S. M., Lü, J. H., Yu, X. H., Chen, G. R.: Design and implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops..IEEE Trans. Circuits Syst. I 59 (2012), 1015-1028. MR 2924533, 10.1109/TCSI.2011.2180429
Reference: [36] Yu, W. G.: Finite-time stabilization of three-dimensional chaotic systems based on CLF..Phys. Lett. A 374 (2010), 3021-3024. Zbl 1237.34093, MR 2660601, 10.1016/j.physleta.2010.05.040
Reference: [37] Yu, Y. G., Zhang, S. C.: Adaptive backstepping synchronization of uncertain chaotic system Chaos..Chaos Solitons Fractals 21 (2004), 643-649. 10.1016/j.chaos.2003.12.067
Reference: [38] Zhang, H., Ma, X. K., Li, M., Zou, J. L.: Controlling and tracking hyperchaotic Rossler system via active backstepping design..Chaos Solitons Fractals 26 (2005), 353-361. Zbl 1153.93381, 10.1016/j.chaos.2004.12.032
Reference: [39] 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 Fractals 39 (2009), 2477-2483. 10.1016/j.chaos.2007.07.017
Reference: [40] Zhu, C. X.: Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters..Appl. Math. Comput. 215 (2009), 557-561. Zbl 1182.37028, MR 2561513, 10.1016/j.amc.2009.05.026
.

Files

Files Size Format View
Kybernetika_49-2013-4_4.pdf 407.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo