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Criteria for global pinning-controllability of complex networks. (English) Zbl 1153.93329
Summary: We study pinning-controllability of networks of coupled dynamical systems. In particular, we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network. The reference trajectory is generated by an exogenous independent oscillator, and pinned nodes are coupled to it through a linear state feedback. We describe the time evolution of the complex dynamical system in terms of the error dynamics. Thereby, we reformulate the pinning-controllability problem as a global asymptotic stability problem. By using Lyapunov-stability theory and algebraic graph theory, we establish tractable sufficient conditions for global pinning-controllability in terms of the network topology, the oscillator dynamics, and the linear state feedback.

MSC:
93B05Controllability
93D20Asymptotic stability of control systems
93C10Nonlinear control systems
93D05Lyapunov and other classical stabilities of control systems
93B11System structure simplification
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[1] Bai, Z.; Demmel, J.; J., A.; Dongarra, H.; Ruhe; Der Vorst, Van: Templates for the solution of algebraic eigenvalue problems: A practical guide. (2000)
[2] Belykh, V.; Belykh, I.; Hasler, M.: Connection graph stability method for synchronized coupled chaotic systems. Physica D 195, No. 1--2, 159-187 (2004) · Zbl 1098.82622
[3] Belykh, I.; Belykh, V.; Nevidin, K.; Hasler, M.: Persistent clusters in lattices of coupled nonidentical chaotic systems. Chaos 13, 165-178 (2003) · Zbl 1080.37525
[4] Belykh, I.; Hasler, M.; Belykh, V.: When symmetrization guarantees synchronization in directed networks. International journal of bifurcation and chaos 17, No. 10, 1-9 (2007) · Zbl 1142.93404
[5] Belykh, I.; Hasler, M.; Lauret, M.; Nijmeijer, H.: Synchronization and graph topology. International journal of bifurcation and chaos 15, No. 11, 3423-3433 (2005) · Zbl 1107.34047
[6] Bernstein, D. S.: Matrix mathematics. (2005) · Zbl 1075.15001
[7] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D.: Complex networks: structure and dynamics. Physics reports 424, 175-308 (2006)
[8] Chen, T.; Liu, X.; Lu, W.: Pinning complex networks by a single controller. IEEE transactions on circuits and systems I 54, No. 6, 1317-1326 (2007)
[9] Friedler, M.: Algebraic connectivity of graphs. Czechoslovak mathematical journal 23, No. 98, 298-305 (1973)
[10] Ghosh, A., & Boyd, S. (2006). Growing well-connected graphs, In Proceedings of the 45th IEEE conference on decision and control (pp. 6605--6611)
[11] Godsil, C.; Royle, G.: Algebraic graph theory. (2001) · Zbl 0968.05002
[12] Grigoriev, R.; Cross, M.; Schuste, H.: Pinning control of spatiotemporal chaos. Physical review letters 79, No. 15, 2795-2798 (1997)
[13] Ipsen, I.C.G., & Nadler, B. Refined perturbation bounds for eigenvalues of hermitian and non-hermitian matrices, Samsi Technical Report no. 2007-2 (unpublished)
[14] Jadbabaie, A.; Lin, J.; Morse, A. S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE transactions on automatic control 48, No. 6, 988-1001 (2003)
[15] Jiang, G. P.; Tang, W. K. S.; Chen, G.: A simple global synchronization criterion for coupled chaotic system. Chaos, solitons & fractals 15, 925-935 (2003) · Zbl 1065.70015
[16] Khalil, H. K.: Nonlinear systems. (2002) · Zbl 1003.34002
[17] Lafferriere, G.; Williams, A.; Caughman, J.; Veerman, J. J. P.: Decentralized control of vehicle formations. Systems & control letters 54, No. 9, 899-910 (2005) · Zbl 1129.93303
[18] Lerescu, A. I.; Contandache, N.; Oancea, S.; Grosu, I.: Collection of master--slave synchronized chaotic systems. Chaos, solitons & fractals 22, 599-604 (2004) · Zbl 1096.93016
[19] Li, R., Duan, Z., & Chen, G. (2007). Cost and effects of pinning control for network synchronization. arXiv:0710.2716v1
[20] Li, X.; Wang, X.; Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE transactions on circuits and systems-I 51, No. 10, 2074-2087 (2004)
[21] Lu, W.: Adaptive dynamical networks via neighborhood information: synchronization and pinning control. Chaos 17, No. 2, 023122 (2007) · Zbl 1159.37366
[22] Rulkov, N. F.: Images of synchronized chaos: experiments with circuits. Chaos 6, 262-279 (1996)
[23] Sorrentino, F.; Di Bernardo, M.; Garofalo, F.; Chen, G.: Controllability of complex networks via pinning. Physical review E 75, 046103 (2007)
[24] Wang, X.; Chen, G.: Pinning control of scale-free dynamical networks. Physica A 310, 521-531 (2002) · Zbl 0995.90008
[25] Wu, C.: Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems. Physics letters A 319, No. 5-6, 495-503 (2003) · Zbl 1029.37018
[26] Xiang, J.; Chen, G.: On the V-stability of complex dynamical networks. Automatica 43, 1049-1057 (2007) · Zbl 05246818