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Liu和Barabasi将现代控制理论应用到线性系统的网络可控性问题上, 提出了最小驱动节点集的计算方法, 解决了复杂网络控制的可计算问题. 针对现实网络中存在的节点因负荷过载而失效的问题, 本文提出了基于节点负荷失效的网络可控性模型. 通过对网络采用介数和Weibull失效模型, 在随机和目标失效机制下进行仿真, 研究结果表明: 维持无标度网络可控性的难度要明显大于随机网络; 在目标节点失效机制下, 即使对网络输入极少的失效信号, 也能极大地破坏网络的可控性; 使高介数节点失效要比使度高节点失效更能破坏网络的可控性, 说明高介数节点在维持网络可控性上发挥着重要作用; 对不同的负荷失效模型, 要合理采取措施, 防止网络发生阶跃性全不可控现象.Liu and Barabasi applied the modern control theory to the network controllability of linear dynamical systems and proposed a method to calculate the minimal set of driver node which controls the states of all nodes in a linear time invariant complex network with any topology. The network controllability model solves the computable problems of the network controllability. Facing the problem of node overloaded failure in real networks, in the paper we investigate the model of network controllability based on node overloaded failure. Through the simulation of betweenness and Weibull failure model, the results demonstrate that the difficulty in maintaining the controllability of SF network is significantly greater than that of ER network. In the target failure mechanism, even if the failure signals input rarely to the networks, they can greatly increase the difficulty of network controllability. Besides, the node failure based high betweenness centrality is more efficient than failure based high degree on damaging network controllability, which indicates the nodes with high betweenness centrality play an important role in maintaining the network controllability. Furthermore, taking the reasonable measures for different load failure model can prevent the networks from inducing a step uncontrollable phenomenon.
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Keywords:
- network controllability /
- structure controllability /
- node failure
[1] Lombardi A, Hörnquist M 2007 Phys. Rev. E 75 056110
[2] Sorrentino F, Bernardo M, Garofalo F, Chen G R 2007 Phys. Rev. E 75 046103
[3] Liu Y Y, Slotine J J, Barabási A L 2011 Nature 473 167
[4] Mller F J, Schuppert A 2011 Nature 478 E4
[5] Egerstedt M 2011 Nature 473 158
[6] Hou L L, Lao S Y, Liu G, Bai L 2012 Chin. Phys. Lett. 29 108901
[7] Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[8] L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512 (in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 物理学报 61 170512]
[9] Lin C T 1974 IEEE Trans. Automatic Control 19 201
[10] Bollobás B 1985 Random Graphs (London: Academic)
[11] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[12] Motter A E 2004 Phys. Rev. Lett. 93 098701
[13] Newman M E J 2001 Proc. Natl. Acad. Sci. 98 404
[14] Moreno Y, Gómez B J, Pacheco A F 2002 Europhys. Lett. 58 630
[15] Erdös P, Rényi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[16] Barabási A L, Albert R 1999 Science 286 509
[17] Pu C L, Pei W J, Andrew M 2012 Physica A 391 4420
[18] Freeman L C 1977 Sociometry 40 35
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[1] Lombardi A, Hörnquist M 2007 Phys. Rev. E 75 056110
[2] Sorrentino F, Bernardo M, Garofalo F, Chen G R 2007 Phys. Rev. E 75 046103
[3] Liu Y Y, Slotine J J, Barabási A L 2011 Nature 473 167
[4] Mller F J, Schuppert A 2011 Nature 478 E4
[5] Egerstedt M 2011 Nature 473 158
[6] Hou L L, Lao S Y, Liu G, Bai L 2012 Chin. Phys. Lett. 29 108901
[7] Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[8] L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512 (in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 物理学报 61 170512]
[9] Lin C T 1974 IEEE Trans. Automatic Control 19 201
[10] Bollobás B 1985 Random Graphs (London: Academic)
[11] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[12] Motter A E 2004 Phys. Rev. Lett. 93 098701
[13] Newman M E J 2001 Proc. Natl. Acad. Sci. 98 404
[14] Moreno Y, Gómez B J, Pacheco A F 2002 Europhys. Lett. 58 630
[15] Erdös P, Rényi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[16] Barabási A L, Albert R 1999 Science 286 509
[17] Pu C L, Pei W J, Andrew M 2012 Physica A 391 4420
[18] Freeman L C 1977 Sociometry 40 35
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