Group synchronization of diffusively coupled harmonic oscillators
Liyun Zhao; Jun Liu; Lan Xiang; Jin Zhou
Kybernetika (2016)
- Volume: 52, Issue: 4, page 629-647
- ISSN: 0023-5954
Access Full Article
topAbstract
topHow to cite
topZhao, Liyun, et al. "Group synchronization of diffusively coupled harmonic oscillators." Kybernetika 52.4 (2016): 629-647. <http://eudml.org/doc/286827>.
@article{Zhao2016,
abstract = {This paper considers group synchronization issue of diffusively directed coupled harmonic oscillators for two cases with nonidentical and identical agent dynamics. For the case of coupled nonidentical harmonic oscillators with positive coupling, it is demonstrated that distributed group synchronization can always be achieved under two kinds of network structures, i. e., the strongly connected graph and the acyclic partition topology with a directed spanning tree. It is interesting to find that the group synchronization states under acyclic partition are some periodic orbits with the same frequency and are simply related with the initial values of certain group regardless of ones of the other groups. For the case of coupled identical harmonic oscillators with positive and negative coupling, some generic algebraic criteria on group synchronization with both local continuous and instantaneous interaction are established respectively. In particular, an explicit expression of group synchronization states in terms of initial values of the agents can be obtained by the property of acyclic partition topology, and so it is very convenient to yield the desired group synchronization in practical application. Finally, numerical examples illustrate and visualize the effectiveness and feasibility of theoretical results.},
author = {Zhao, Liyun, Liu, Jun, Xiang, Lan, Zhou, Jin},
journal = {Kybernetika},
keywords = {group synchronization; coupled harmonic oscillators; directed topology; acyclic partition; group synchronization; coupled harmonic oscillators; directed topology; acyclic partition},
language = {eng},
number = {4},
pages = {629-647},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Group synchronization of diffusively coupled harmonic oscillators},
url = {http://eudml.org/doc/286827},
volume = {52},
year = {2016},
}
TY - JOUR
AU - Zhao, Liyun
AU - Liu, Jun
AU - Xiang, Lan
AU - Zhou, Jin
TI - Group synchronization of diffusively coupled harmonic oscillators
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 4
SP - 629
EP - 647
AB - This paper considers group synchronization issue of diffusively directed coupled harmonic oscillators for two cases with nonidentical and identical agent dynamics. For the case of coupled nonidentical harmonic oscillators with positive coupling, it is demonstrated that distributed group synchronization can always be achieved under two kinds of network structures, i. e., the strongly connected graph and the acyclic partition topology with a directed spanning tree. It is interesting to find that the group synchronization states under acyclic partition are some periodic orbits with the same frequency and are simply related with the initial values of certain group regardless of ones of the other groups. For the case of coupled identical harmonic oscillators with positive and negative coupling, some generic algebraic criteria on group synchronization with both local continuous and instantaneous interaction are established respectively. In particular, an explicit expression of group synchronization states in terms of initial values of the agents can be obtained by the property of acyclic partition topology, and so it is very convenient to yield the desired group synchronization in practical application. Finally, numerical examples illustrate and visualize the effectiveness and feasibility of theoretical results.
LA - eng
KW - group synchronization; coupled harmonic oscillators; directed topology; acyclic partition; group synchronization; coupled harmonic oscillators; directed topology; acyclic partition
UR - http://eudml.org/doc/286827
ER -
References
top- Ballard, L., Cao, C. Y., Ren, W., 10.1049/iet-cta.2009.0053, IET Control Theory Appl. 4 (2010), 806-816. MR2758795DOI10.1049/iet-cta.2009.0053
- Chen, Y., L, J. H., Yu, X. H., Lin, Z. L., 10.1137/110850116, SIAM J. Control Optim. 51 (2013), 3274-3301. MR3090151DOI10.1137/110850116
- Cheng, S., Ji, C. J., Zhou, J., 10.1088/0031-8949/84/03/035006, Physica Scripta 84 (2011), 035006. Zbl1262.34057DOI10.1088/0031-8949/84/03/035006
- Desoer, C., Vidyasagar, M., Feedback Systems: Input-output Properties., Academic, New York 1975. Zbl1153.93015MR0490289
- Godsil, C., Royle, G., 10.1007/978-1-4613-0163-9, Springer-Verlag, London 2001. Zbl0968.05002MR1829620DOI10.1007/978-1-4613-0163-9
- He, W. L., Qian, F., Lam, J., Chen, G. R., Han, Q. L., Kurths, J., 10.1016/j.automatica.2015.09.028, Automatica 62 (2015), 249-262. Zbl1330.93011MR3423996DOI10.1016/j.automatica.2015.09.028
- He, W. L., Zhang, B., Han, Q. L., Qian, F., Kurths, J., Cao, J. D., 10.1109/tcyb.2015.2514119, IEEE Trans. Cybernetics (2016), 1-12. DOI10.1109/tcyb.2015.2514119
- Hong, Y. G., Hu, J. P., Gao, L. X., 10.1016/j.automatica.2006.02.013, Automatica 42 (2006), 1177-1182. Zbl1117.93300MR2230987DOI10.1016/j.automatica.2006.02.013
- Horn, R., Johnson, C. R., 10.1002/zamm.19870670330, Cambridge University Press, Cambridge 1990. Zbl0801.15001MR1084815DOI10.1002/zamm.19870670330
- Liu, J., Zhou, J., 10.1080/00207179.2014.985717, Int. J. Control 88 (2015), 910-919. Zbl1316.93005MR3325386DOI10.1080/00207179.2014.985717
- Lu, S. J., Chen, L., A general synchronization method of chaotic communication system via kalman filtering., Kybernetika 44 (2008), 43-52. MR2405054
- Lu, W. L., Liu, B., Chen, T. P., 10.1063/1.3329367, Chaos 20 (2010), 013120. Zbl1311.34117MR2730167DOI10.1063/1.3329367
- Ma, M. H., Zhang, H., Cai, J. P., Zhou, J., Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch., Kybernetika 49 (2013), 539-553. Zbl1274.70039MR3117913
- Qin, J. H., Yu, C. B., 10.1016/j.automatica.2013.06.017, Automatica 49 (2013), 2898-2905. MR3084481DOI10.1016/j.automatica.2013.06.017
- Ren, W., 10.1016/j.automatica.2008.05.027, Automatica 44 (2008), 3195-3200. Zbl1153.93421MR2531426DOI10.1016/j.automatica.2008.05.027
- Ren, W., Cao, Y. C., Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues., Springer-Verlag, London 2011. Zbl1225.93003
- Slotine, J. J. E., Li, W. P., Applied Nonlinear Control., Prentice Hall, N.J. 1991. Zbl0753.93036
- Su, H. S., Wang, X. F., Lin, Z. L., 10.1016/j.automatica.2009.05.026, Automatica 45 (2009), 2286-2291. Zbl1179.93102MR2890789DOI10.1016/j.automatica.2009.05.026
- Su, H. S., Chen, M., Wang, X. F., Wang, H. W., Valeyev, N. V., 10.1049/iet-cta.2012.0910, IET Control Theory Appl. 7 (2013), 765-772. MR3100186DOI10.1049/iet-cta.2012.0910
- Wang, K. H., Fu, X. C., Li, K. Z., 10.1063/1.3125714, Chaos 19 (2009), 023106. Zbl1309.34107MR2548747DOI10.1063/1.3125714
- Wu, W., Zhou, W. J., Chen, T. P., 10.1109/tcsi.2008.2003373, IEEE Trans. Circuits Syst. I. Reg. Pap. 56 (2009), 819-839. MR2724977DOI10.1109/tcsi.2008.2003373
- Xia, W. G., Cao, M., 10.1016/j.automatica.2011.08.043, Automatica 47 (2011), 2395-2405. Zbl1228.93015MR2886867DOI10.1016/j.automatica.2011.08.043
- Yang, T., Impulsive Control Theory., Springer 2001. Zbl0996.93003MR1850661
- Yu, W. W., Chen, G. R., Cao, M., Kurths, J., 10.1109/tsmcb.2009.2031624, IEEE T. Syst. Man Cy. B 40 (2010), 881-891. DOI10.1109/tsmcb.2009.2031624
- Yu, C. B., Qin, J. H., Gao, H. J., 10.1016/j.automatica.2014.07.013, Automatica 50 (2014), 2341-2349. Zbl1297.93019MR3256724DOI10.1016/j.automatica.2014.07.013
- Yu, J. Y., Wang, L., Group consensus of multi-agent systems with undirected communication graphs., In: Proc. 7th Asian Control Conference 2009, pp. 105-110.
- Zhang, H., Zhou, J., 10.1016/j.sysconle.2012.10.001, Syst. Control Lett. 61 (2012), 1277-1285. Zbl1256.93064MR2998215DOI10.1016/j.sysconle.2012.10.001
- Zhao, L. Y., Wu, Q. J., Zhou, J., 10.1109/chicc.2014.6895598, In: Proc. 33rd Chinese Control Conference 2014, pp. 3950-3954. DOI10.1109/chicc.2014.6895598
- Zhou, J., Zhang, H., Xiang, L., Wu, Q. J., 10.1016/j.automatica.2012.05.022, Automatica 48 (2012), 1715-1721. Zbl1267.93008MR2950421DOI10.1016/j.automatica.2012.05.022
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.