| Title:
|
Drive network to a desired orbit by pinning control (English) |
| Author:
|
Wu, Quanjun |
| Author:
|
Zhang, Hua |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
150-172 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology. (English) |
| Keyword:
|
complex dynamical network |
| Keyword:
|
pinning control |
| Keyword:
|
directed coupling |
| Keyword:
|
time delay |
| Keyword:
|
DCN oscillator |
| MSC:
|
34D06 |
| MSC:
|
34K20 |
| MSC:
|
70K40 |
| MSC:
|
74H65 |
| idZBL:
|
Zbl 06433837 |
| idMR:
|
MR3333838 |
| DOI:
|
10.14736/kyb-2015-1-0150 |
| . |
| Date available:
|
2015-03-23T18:58:34Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144207 |
| . |
| Reference:
|
[1] Arenas, A., Diaz-Guilera, A., Kurths, J., Morenob, Y., Zhoug, C.: Synchronization in complex networks..Phys. Rep. 469 (2008), 93-153. MR 2477097, 10.1016/j.physrep.2008.09.002 |
| Reference:
|
[2] Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics..Phys. Rep. 424 (2006), 175-308. MR 2193621, 10.1016/j.physrep.2005.10.009 |
| Reference:
|
[3] Cai, S. M., Zhou, J., Xiang, L., Liu, Z. R.: Robust impulsive synchronization of complex delayed dynamical networks..Phys. Lett. A 372 (2008), 4990-4995. Zbl 1221.34075, 10.1016/j.physleta.2008.05.077 |
| Reference:
|
[4] Cai, S. M., He, Q. B., Hao, J. J., Liu, Z. R.: Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes..Phys. Lett. A 374 (2010), 2539-2550. Zbl 1236.05185, MR 2640029, 10.1016/j.physleta.2010.04.023 |
| Reference:
|
[5] Chen, T. P., Liu, X. W., Lu, W. L.: Pinning complex networks by a single controller..IEEE Trans. Circuits Syst. I. Reg. Pap. 54 (2007), 1317-1326. MR 2370589, 10.1109/tcsi.2007.895383 |
| Reference:
|
[6] Chen, Y., Lü, J. H., Yu, X. H., Lin, Z. L.: Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices..SIAM J. Control Optim. 51 (2013), 3274-3301. Zbl 1275.93005, MR 3090151, 10.1137/110850116 |
| Reference:
|
[7] Chen, Y., Lü, J. H., Lin, Z. L.: Consensus of discrete-time multi-agent systems with transmission nonlinearity..Automatica 49 (2013), 1768-1775. MR 3049226, 10.1016/j.automatica.2013.02.021 |
| Reference:
|
[8] Guo, W. L., Austin, F., Chen, S. H., Sun, W.: Pinning synchronization of the complex networks with non-delayed and delayed coupling..Phys. Lett. A 373 (2009), 1565-1572. Zbl 1228.05266, MR 2513417, 10.1016/j.physleta.2009.03.003 |
| Reference:
|
[9] Li, Z., Lee, J. J.: New eigenvalue based approach to synchronization in asymmetrically coupled networks..Chaos 17 (2007), 043117-043117. Zbl 1163.37347, MR 2380036, 10.1063/1.2804525 |
| Reference:
|
[10] Li, X., Wang, X. F., Chen, G. R.: Pinning a complex dynamical network to its equilibrium..IEEE Trans. Circuits Syst. I. Reg. Pap. 51 (2004), 2074-2087. MR 2096915, 10.1109/tcsi.2004.835655 |
| Reference:
|
[11] 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:
|
[12] Liu, B., Lu, W. L., Chen, T. P.: Pinning consensus in networks of multiagents via a single impulsive controller..IEEE Trans. Neural Netw. Learn. Syst. 24 (2013), 1141-1149. 10.1109/tnnls.2013.2247059 |
| Reference:
|
[13] Lu, H. T.: Chaotic attractors in delayed neural networks..Phys. Lett. A 298 (2002), 109-116. Zbl 0995.92004, 10.1016/s0375-9601(02)00538-8 |
| Reference:
|
[14] Lu, W. L.: Adaptive dynamical networks via neighborhood information: synchronization and pinning control..Chaos 17 (2007), 023122-023122. Zbl 1159.37366, MR 2340616, 10.1063/1.2737829 |
| Reference:
|
[15] Lu, W. L., Chen, T. P.: New approach to synchronization analysis of linearly coupled ordinary differential systems..Phys. D 213 (2006), 214-230. Zbl 1105.34031, MR 2201200, 10.1016/j.physd.2005.11.009 |
| Reference:
|
[16] Lu, S. J, Chen, L.: A general synchronization method of chaotic communication system via kalman filtering..Kybernetika 44 (2008), 43-52. MR 2405054 |
| Reference:
|
[17] Lu, J. Q., Wang, Z. D., Cao, J. D., Ho, D. W. C., Kurths, J.: Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay..Int. J. Bifurc. Chaos 22 (2012), 1250176-1250176. Zbl 1270.92006, 10.1142/s0218127412501763 |
| Reference:
|
[18] Lü, J. H., Yu, X., Chen, G. R., Cheng, D. Z.: Characterizing the synchronizability of small-world dynamical networks..IEEE Trans. Circuits Syst. I. Reg. Pap. 51 (2004), 787-796. MR 2066214, 10.1109/tcsi.2004.823672 |
| Reference:
|
[19] Lü, J. H., Yu, X., Chen, G. R.: Chaos synchronization of general complex dynamical networks..Phys. A 334 (2004), 281-302. MR 2044940, 10.1016/j.physa.2003.10.052 |
| Reference:
|
[20] Lü, J. H., Chen, G. R.: A time-varying complex dynamical network model and its controlled synchronization criteria..IEEE Trans. Automat. Control 50 (2005), 841-846. MR 2142000, 10.1109/tac.2005.849233 |
| Reference:
|
[21] 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. Zbl 1274.70039, MR 3117913 |
| Reference:
|
[22] Porfiri, M., Bernardo, M. di: Criteria for global pinning-controllability of complex networks..Automatica 44 (2008), 3100-3106. Zbl 1153.93329, MR 2531411, 10.1016/j.automatica.2008.05.006 |
| Reference:
|
[23] Porfiri, M., Fiorilli, F.: Node-to-node pinning control of complex networks..Chaos 19 (2009), 013122-013122. MR 2513766, 10.1063/1.3080192 |
| Reference:
|
[24] Song, Q., Cao, J. D.: On pinning synchronization of directed and undirected complex dynamical networks..IEEE Trans. Circuits Syst. I. Reg. Pap. 57 (2010), 672-680. MR 2729966, 10.1109/tcsi.2009.2024971 |
| Reference:
|
[25] Sorrentino, F., Bernardo, M., Garofalo, F., Chen, G. R.: Controllability of complex networks via pinning..Phys. Rev. E 75 (2007), 046103-046103. 10.1103/physreve.75.046103 |
| Reference:
|
[26] Tang, Y., Wang, Z. D., Fang, J A.: Pinning control of fractional-order weighted complex networks..Chaos 19 (2009), 013112-013112. MR 2513760, 10.1063/1.3068350 |
| Reference:
|
[27] Wang, X. F., Chen, G. R.: Synchronization in scale-free dynamical networks: robustness and fragility..IEEE Trans. Circuits Syst. I. Fundam. Theory Appl. 49 (2002), 54-62. MR 1874226, 10.1109/81.974874 |
| Reference:
|
[28] Wang, X. F., Chen, G. R.: Synchronization in small-world dynamical networks..Int. J. Bifurc. Chaos 12 (2002), 187-192. 10.1142/s0218127402004292 |
| Reference:
|
[29] Wang, X. F., Chen, G. R.: Pinning control of scale-free dynamical networks..Phys. A 310 (2002), 521-531. Zbl 0995.90008, MR 1946327, 10.1016/s0378-4371(02)00772-0 |
| Reference:
|
[30] Wu, Y. Y., Wei, W., Li, G. Y., Xiang, J.: Pinning control of uncertain complex networks to a homogeneous orbit..IEEE Trans. Circuits Syst. II Exp. Briefs 56 (2009), 235-239. 10.1109/tcsii.2009.2015350 |
| Reference:
|
[31] Wu, W., Zhou, W. J., Chen, T. P.: Cluster synchronization of linearly coupled complex networks under pinning control..IEEE Trans. Circuits Syst. I. Reg. Pap. 56 (2009), 829-839. MR 2724977, 10.1109/tcsi.2008.2003373 |
| Reference:
|
[32] Xia, W. G., Cao, J. D.: Pinning synchronization of delayed dynamical networks via periodically intermittent control..Chaos 19 (2009), 013120-013120. MR 2513764, 10.1063/1.3071933 |
| Reference:
|
[33] Xiang, J., Chen, G. R.: Analysis of pinning-controlled networks: a renormalization approach..IEEE Trans. Automat. Control 54 (2009), 1869-1875. MR 2552820, 10.1109/tac.2009.2020668 |
| Reference:
|
[34] Xiang, L. Y., Liu, Z. X., Chen, Z. Q., Chen, F., Yuan, Z. Z.: Pinning control of complex dynamical networks with general topology..Phys. A 379 (2007), 298-306. 10.1016/j.physa.2006.12.037 |
| Reference:
|
[35] Xiang, L. Y., Zhu, J. J. H.: On pinning synchronization of general coupled networks..Nonlin. Dynam. 64 (2011), 339-348. MR 2803214, 10.1007/s11071-010-9865-5 |
| Reference:
|
[36] Yu, W. W., Chen, G. R., Lü, J. H.: On pinning synchronization of complex dynamical networks..Automatica 45 (2009), 429-435. Zbl 1158.93308, MR 2527339, 10.1016/j.automatica.2008.07.016 |
| Reference:
|
[37] Zhou, J., Chen, T. P.: Synchronization in general complex delayed dynamical networks..IEEE Trans. Circuits Syst. I. Reg. Pap. 53 (2006), 733-744. MR 2212426, 10.1109/tcsi.2005.859050 |
| Reference:
|
[38] Zhou, J., Lu, J. A., Lü, J. H.: Adaptive synchronization of an uncertain complex dynamical network..IEEE Trans. Automat. Control 51 (2006), 652-656. MR 2228029, 10.1109/tac.2006.872760 |
| Reference:
|
[39] Zhou, J., Lu, J. A., Lü, J. H.: Pinning adaptive synchronization of a general complex dynamical network..Automatica 44 (2008), 996-1003. Zbl 1158.93339, MR 2530942, 10.1016/j.automatica.2007.08.016 |
| Reference:
|
[40] Zhou, J., Wu, Q. J., Xiang, L.: Pinning complex delayed dynamical networks by a single impulsive controller..IEEE Trans. Circuits Syst. I. Reg. Pap. 58 (2011), 2882-2893. MR 2907084, 10.1109/tcsi.2011.2161363 |
| Reference:
|
[41] Zhou, J., Wu, Q. J., Xiang, L.: Impulsive pinning complex dynamical networks and applications fo firing neuronal synchronization..Nonlin. Dynam. 69 (2012), 1393-1403. MR 2943393, 10.1007/s11071-012-0355-9 |
| Reference:
|
[42] Zhou, J., Wu, Q. J., Xiang, L., Cai, S. M., Liu, Z. R.: Impulsive synchronization seeking in complex delayed dynamical networks..Nonlin. Anal.: Hybrid Syst. 5 (2011), 513-524. MR 2819260, 10.1016/j.nahs.2010.10.013 |
| . |
