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Decentralized control and synchronization of time-varying complex dynamical network. (English) Zbl 1158.34332
Summary: A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller makes use of the information on the corresponding node’s dynamics and the resulting overall controller is composed of those sub-controllers. The overall controller can be obtained by means of a combination of typical control designs and appropriate parametric tuning for each isolated node. Several numerical simulation examples are given to illustrate the feasibility and the efficiency of the proposed control design.

34D20Stability of ODE
65L99Numerical methods for ODE
70G60Dynamical systems methods for dynamical systems
70K99Nonlinear dynamics (general mechanics)
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[1] A.-L. Barabási and R. Albert: Emergence of scaling in random networks. Science 286 (1999), 509-512. · Zbl 1226.05223 · doi:10.1126/science.286.5439.509
[2] Changchun Hua, Xinping Guan, and Peng Shi: Decentralized robust model reference adaptive control for interconnected time-delay systems. J. Comput. Appl. Math. 193 (2006), 383-396. · Zbl 1136.93303 · doi:10.1016/j.cam.2005.06.024
[3] Chaohong Cai and Guanrong Chen: Synchronization of complex dynamical networks by the incremental ISS approach. Phys. A 371 (2006), 754-766.
[4] Chunguang Li and Guanrong Chen: Synchronization in general complex dynamical networks with coupling delays. Phys. A 343 (2004), 263-278.
[5] P. Erdös and A. Rényi: On the evolution of random graphs. Publ. Math. Inst. Hautes Études Sci. 5 (1959), 17-60.
[6] Guo-Ping Jiang, Wallace Kit-Sang Tang, and Guanrong Chen: A state-observer-based approach for synchronization in complex dynamical networks. IEEE Trans. Circuits and Systems. I Regul. Pap. 53 (2006), 2739-2745.
[7] Jianshe Wu and Licheng Jiao: Observer-based synchronization in complex dynamical networks with nonsymmetric coupling. Phys. A 386 (2007), 469-480. · Zbl 1178.34056 · doi:10.1016/j.physd.2008.03.002
[8] Jin Zhou and Tianping Chen: Synchronization in general complex delayed dynamical networks. IEEE Trans. Circuits and Systems. I Regul. Pap. 53 (2006), 733-744.
[9] Jin Zhou, Junan Lu, and Jinhu Lü: Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Automat. Control 51 (2006), 652-656.
[10] Jinhu Lü and Guangrong Chen: A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Automat. Control 50 (2005), 841-846.
[11] K. Li and C. H. Lai: Adaptive-impulsive synchronization of uncertain complex dynamical networks. Phys. Lett. A 372 (2008), 1601-1606. · Zbl 1217.05210 · doi:10.1016/j.physleta.2007.10.020
[12] D. J. Watts and S. H. Strogatz: Collective dynamics of small-world networks. Nature 393 (1998), 440-442.
[13] Xiao Fan Wang and Guanrong Chen: Pinning control of scale-free dynamical networks. Phys. A 324 (2004), 166-178.
[14] Xiao Fan Wang and Guangrong Chen: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuits and Systems. I Regul. Pap. 49 (2002), 54-62.
[15] Xiaoqun Wu: Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay. Phys. A 387 (2008), 997-1008.
[16] Xiang Li and Guanrong Chen: Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Trans. Circuits and Systems. I Regul. Pap. 50 (2003), 1381-1390.
[17] Xing-Gang Yan and Guan-Zhong Dai: Decentralized output feedback robust control for nonlinear Large-scale systems. Automatica 34 (1998), 1469-1472. · Zbl 0934.93007 · doi:10.1016/S0005-1098(98)00090-9
[18] Zhengping Fan and Guangrong Chen: Pinning control of scale-free complex networks. IEEE Internat. Symposium on Circuits and Systems, Madison 2005, pp. 284-287.
[19] Zhi Li and Guanrong Chen: Global synchronization and asymptotic stability of complex dynamical networks. IEEE Trans. Circuits Syst. I Regul. Pap. 53 (2006), 28-33.
[20] Zhi Li and Guanrong Chen: Robust adaptive synchronization of uncertain dynamical networks. Phys. Lett. A 310 (2002), 521-531. · Zbl 1123.93316
[21] ZhiHong Guan and Hao Zhang: Stabilization of complex network with hybrid impulsive and switching control. Chaos Solitons Fractals 37 (2008), 1372-1382. · Zbl 1142.93423 · doi:10.1016/j.chaos.2006.10.064
[22] Zhisheng Duan, Jinzhi Wang, Guanrong Chen, and Lin Huang: Stability analysis and decentralized control of a class of complex dynamical networks. Automatica 44 (2008), 1028-1035. · Zbl 1283.93017 · doi:10.1016/j.automatica.2007.08.005