| Title:
|
Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch (English) |
| Author:
|
Ma, Mihua |
| Author:
|
Zhang, Hua |
| Author:
|
Cai, Jianping |
| Author:
|
Zhou, Jin |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
539-553 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is concerned with impulsive practical synchronization in a class of n-dimensional nonautonomous dynamical systems with parameter mismatch. Some simple yet general algebraic synchronization criteria are derived based on the developed practical stability theory on impulsive dynamical systems. A distinctive feature of this work is that the impulsive control strategy is used to make n-dimensional nonautonomous dynamical systems with parameter mismatch achieve practical synchronization, where the parameter mismatch likewise exist in both system parameters and external excitation ones, and the synchronization error bound can be estimated by an analytical expression. Subsequently, the obtained results are applied to a typical gyrostat system, and numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control technique. (English) |
| Keyword:
|
practical synchronization |
| Keyword:
|
impulsive control |
| Keyword:
|
$n$-dimensional nonautonomous systems |
| Keyword:
|
parameter mismatch |
| Keyword:
|
gyrostat system |
| MSC:
|
70K40 |
| MSC:
|
74H65 |
| . |
| Date available:
|
2013-09-17T16:24:24Z |
| Last updated:
|
2013-09-17 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143444 |
| . |
| Reference:
|
[1] V. Astakhov, V.: Effect of parameter mismatch on the mechanism of chaos synchronization loss in coupled systems..Phys. Rev. E 58 (1998), 5620-5628. 10.1103/PhysRevE.58.5620 |
| Reference:
|
[2] Cai, J. P., Ma, M. H., Wu, X. F.: Synchronization of a class of master-slave non-autonomous chaotic systems with parameter mismatch via sinusoidal feedback control..Internat. J. Mod. Phys. B 25 (2011), 2195-2215. 10.1142/S0217979211100254 |
| Reference:
|
[3] Cai, S. M., Hao, J. J., Liu, Z. G.: Chaos quasi-synchronization induced by impulses with parameter mismatches..Chaos 21 (2011), 023112. MR 2849960 |
| Reference:
|
[4] Chen, G., Zhou, J., Čelikovský, C.: On LaSalle's invariance principle and its application to robust synchronization of vector Lienard equations..IEEE Trans. Automat. Control 50 (2005), 869-874. MR 2142006, 10.1109/TAC.2005.849250 |
| Reference:
|
[5] Chen, Y., Wu, X. F., Gui, Z. F.: Global robust synchronization of a class of nonautonomous chaotic systems with parameter mismatch via variable substitution control..Internat. J. Bifur. Chaos 21 (2011), 1369-1382. Zbl 1248.34077, MR 2819827, 10.1142/S0218127411029239 |
| Reference:
|
[6] Ge, Z. M., Leu, W. Y.: Anti-control of chaos of two-degrees-of-freedom loudspeaker system and chaos synchronization of different order systems..Chaos, Solitons and Fractals 20 (2004), 503-521. Zbl 1048.37077, 10.1016/j.chaos.2003.07.001 |
| Reference:
|
[7] Ge, Z. M., Lin, T. N.: Chaos, chaos control and synchronization of a gyrostat system..J. Sound Vibration 251 (2002), 519-542. Zbl 1237.70019, MR 1897547, 10.1006/jsvi.2001.3995 |
| Reference:
|
[8] Ge, Z. M., Yu, T. C., Chen, Y. S.: Chaos synchronization of a horizontal platform system..J. Sound Vibration 268 (2003), 731-749. 10.1016/S0022-460X(02)01607-3 |
| Reference:
|
[9] Horn, R. A., Johnson, C. R.: Matrix Analysis..Cambridge University, Cambridge 1985. Zbl 0801.15001, MR 0832183 |
| Reference:
|
[10] Huang, T. W., Li, C. D., Liao, X. F.: Synchronization of a class of coupled chaotic delayed systems with parameter mismatch..Chaos 17 (2007), 033121. Zbl 1163.37335, MR 2356975, 10.1063/1.2776668 |
| Reference:
|
[11] Jalnine, A., Kim, S. Y.: Characterization of the parameter-mismatching effect on the loss of chaos synchronization..Phys. Rev. E 65 (2002), 026210-026216. 10.1103/PhysRevE.65.026210 |
| Reference:
|
[12] Koofigar, H. R., Sheikholeslam, F., Hosseinnia, S.: Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua's circuit..Chaos 21 (2011), 043134. 10.1063/1.3671969 |
| Reference:
|
[13] Liang, H. T., Wang, Z., Yue, Z. M., Lu, R. H.: Generallized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication..Kybernetika 48 (2012), 190-205. MR 2954320 |
| Reference:
|
[14] Lu, S. J., Chen, L.: A general synchronization method of chaotic communication system via kalman filtering..Kybernetika 44 (2008), 43-52. MR 2405054 |
| Reference:
|
[15] Ma, M. H., Cai, J. P.: Synchronization criteria for coupled chaotic systems with parameter mismatches..Internat. J. Mod. Phys. B 25 (2011), 2493-2506. MR 2822998, 10.1142/S0217979211100916 |
| Reference:
|
[16] Ma, M. H., Zhou, J., Cai, J. P.: Practical synchronization of second-order nonautonomous systems with parameter mismatch and its applications..Nonlinear Dyn. 69 (2012), 3, 1285-1292. Zbl 1258.34126, MR 2943385 |
| Reference:
|
[17] Pecora, L. M., Carroll, T. L.: Synchronizationin chaotic systems..Phys. Rev. Lett. 64 (1990), 821-824. MR 1038263, 10.1103/PhysRevLett.64.821 |
| Reference:
|
[18] Wang, J. G., Cai, J. P., Ma, M. H., Feng, J. C.: Synchronization with error bound of non-identical forced oscillators..Kybernetika 44 (2008), 534-545. Zbl 1173.70009, MR 2459071 |
| Reference:
|
[19] Wang, L. P., Yuan, Z. T., Chen, X. H., Zhou, Z. F.: Lag synchronization of chaotic systems with parameter mismatches..Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 987-992. Zbl 1221.37226, MR 2725820, 10.1016/j.cnsns.2010.04.029 |
| Reference:
|
[20] Wu, X. F., Cai, J. P., Wang, M. H.: Robust synchronization of chaotic horizontal platform systems with phase difference..J. Sound Vibration 305 (2007), 481-491. Zbl 1242.93123, MR 2324743, 10.1016/j.jsv.2007.04.034 |
| Reference:
|
[21] Yang, T.: Impulsive Control Theory..Springer, Berlin 2001. Zbl 0996.93003, MR 1850661 |
| Reference:
|
[22] Zhang, W., Huang, J. J., Wei, P. C.: Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control..Appl. Math. Model. 35 (2011), 612-620. Zbl 1205.93125, MR 2718458, 10.1016/j.apm.2010.07.009 |
| Reference:
|
[23] Zhou, J., Xiang, L., Liu, Z. R.: Global synchronization in general complex delayed dynamical networks and its applications..Phys. A 385 (2007), 729-742. MR 2584888, 10.1016/j.physa.2007.07.006 |
| Reference:
|
[24] Zhu, Z. L., Li, S. P., Yu, H.: A new approach to generallized chaos synchronization based on the stability of the error system..Kybernetika 44 (2008), 492-500. MR 2459067 |
| . |
