×

Topology identification and adaptive synchronization of uncertain complex networks with non-derivative and derivative coupling. (English) Zbl 1202.93023

Summary: This paper proposes an approach to identify the topological structure and unknown parameters for uncertain general complex networks with non-derivative and derivative coupling. By designing effective adaptive controller, the unknown topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously in the process of synchronization. Several useful criteria for synchronization are given. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results obtained in this paper.

MSC:

93B30 System identification
93C15 Control/observation systems governed by ordinary differential equations
93B52 Feedback control
93C40 Adaptive control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavezf, M.; Hwanga, U., Complex networks: structure and dynamics, Physics Reports, 424, 4-5, 175-308 (2006) · Zbl 1371.82002
[2] Li, X.; Chen, G., Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint, IEEE Transaction on Circuits and Systems I, 50, 11, 1381-1390 (2003) · Zbl 1368.37087
[3] Lü, J.; Yu, X.; Chen, G., Chaos synchronization of general complex dynamical networks, Physica A, 334, 1-2, 281-302 (2004)
[4] Zhou, J.; Chen, T.; Xiang, L., Adaptive synchronization of coupled chaotic systems based on parameters identification and its applications, International Journal of Bifurcation and Chaos, 16, 2923-2933 (2006) · Zbl 1142.34387
[5] Zhou, J.; Xiang, L.; Liu, Z., Global synchronization in general complex delayed dynamical networks and its applications, Physica A, 385, 2, 729-742 (2007)
[6] Ma, Z.; Liu, Z.; Zhang, G., A new method to realize cluster synchronization in connected chaotic networks, Chaos, 16, 2, 023103 (2006) · Zbl 1146.37330
[7] Kocarev, L.; Amato, P., Synchronization in power-law networks, Chaos, 15, 2, 024101 (2005) · Zbl 1080.37106
[8] Wang, X.; Chen, G., Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Transaction on Circuits and Systems I, 49, 1, 54-62 (2002) · Zbl 1368.93576
[9] D. Watts, S. Strogatz, Collective dynamics of ‘small-world’ networks, Nature 391 (1998) 440-442.; D. Watts, S. Strogatz, Collective dynamics of ‘small-world’ networks, Nature 391 (1998) 440-442. · Zbl 1368.05139
[10] Barabasi, A.; Albert, R., Emergence of scaling in random networks, Science, 286, 509-512 (1999) · Zbl 1226.05223
[11] Strogatz, S., Exploring complex networks, Nature, 410, 268-276 (2001) · Zbl 1370.90052
[12] Huang, D., Adaptive feedback control algorithm, Physical Review E, 73, 6, 066204 (2006) · Zbl 1244.93064
[13] Wu, X., Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay, Physica A, 387, 4, 997-1008 (2008)
[14] Yu, D.; Righero, M.; Kocarev, L., Estimating topology of network, Physical Review Letters, 97, 18, 188701 (2006)
[15] Zhou, J.; Lu, J., Topology identification of weighted complex dynamical networks, Physica A, 386, 1, 481-491 (2007)
[16] Lu, J.; Cao, J., Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters, Chaos, 15, 4, 043901 (2005) · Zbl 1144.37378
[17] Yu, W.; Cao, J., Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks, Chaos, 16, 2, 023119 (2006) · Zbl 1146.93371
[18] Wu, Z.; Li, K.; Fu, X., Parameter identification of dynamical networks with community structure and multiple coupling delays, Communications in Nonlinear Science and Numerical Simulation, 15, 1, 3587-3592 (2010) · Zbl 1222.93058
[19] Xu, Y.; Zhou, W.; Fang, J.; Lu, H., Structure identification and adaptive synchronization of uncertain general complex dynamical networks, Physics Letters A, 374, 2, 272-278 (2009) · Zbl 1234.05219
[20] Zhang, Q.; Lu, J.; Lü, J.; Tse, C., Adaptive feedback synchronization of a general complex dynamical network with delayed nodes, IEEE Transactions on Circuits and Systems II, 55, 2, 183-187 (2008)
[21] Zhou, J.; Lu, J.; Lü, J., Adaptive synchronization of an uncertain complex dynamical network, IEEE Transactions on Automatic Control, 51, 4, 652-656 (2006) · Zbl 1366.93544
[22] Zhou, J.; Lu, J.; Lü, J., Pinning adaptive synchronization of a general complex dynamical network, Automatica, 44, 4, 996-1003 (2008) · Zbl 1283.93032
[23] Liu, H.; Lu, J.; Lü, J., Structure identification of uncertain general complex dynamical networks with time delay, Automatica, 45, 8, 1799-1807 (2009) · Zbl 1185.93031
[24] Tang, H.; Chen, L.; Lu, J.; Tse, C., Adaptive synchronization between two complex networks with nonidentical topological structures, Physica A, 387, 22, 5623-5630 (2008)
[25] Guo, W.; Chen, S.; Sun, W., Topology identification of the complex networks with non-delayed and delayed coupling, Physics Letters A, 373, 41, 3724-3729 (2009) · Zbl 1232.05218
[26] Sun, W.; Chen, S.; Guo, W., Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling, Physics Letters A, 372, 42, 6340-6346 (2008) · Zbl 1225.05223
[27] Tang, Y.; Qiu, R.; Fang, J.; Miao, Q.; Xia, M., Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays, Physics Letters A, 372, 42, 4425-4433 (2008) · Zbl 1221.82078
[28] Tang, Y.; Fang, J., Synchronization of N-coupled fractional-order chaotic systems with ring connection, Communications in Nonlinear Science and Numerical Simulation, 15, 2, 401-412 (2010) · Zbl 1221.34103
[29] Lorenz, E., Deterministic non-periodic flow, Journal of the Atmospheric Sciences, 20, 130-141 (1963) · Zbl 1417.37129
[30] Lü, J.; Chen, G., A new chaotic attractor coined, International Journal of Bifurcation and Chaos, 12, 3, 659-661 (2002) · Zbl 1063.34510
[31] Chen, G.; Ueta, T., Yet another chaotic attractor, International Journal of Bifurcation and Chaos, 9, 1465-1466 (1999) · Zbl 0962.37013
[32] Liu, C.; Liu, T.; Liu, L.; Liu, K., A new chaotic attractor, Chaos, Solitons and Fractals, 22, 5, 1031-1038 (2004) · Zbl 1060.37027
[33] Zhou, W.; Xu, Y.; Lu, H.; Pan, L., On dynamics analysis of a new chaotic attractor, Physics Letters A, 372, 36, 5773-5777 (2008) · Zbl 1223.37045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.