Jalili Mahdi, Askari Sichani Omid, Yu Xinghuo
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran and School of Electrical and Computer Engineering, RMIT University, Melbourne 3001, Australia.
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012803. doi: 10.1103/PhysRevE.91.012803. Epub 2015 Jan 5.
Controlling networked structures has many applications in science and engineering. In this paper, we consider the problem of pinning control (pinning the dynamics into the reference state), and optimally placing the driver nodes, i.e., the nodes to which the control signal is fed. Considering the local controllability concept, a metric based on the eigenvalues of the Laplacian matrix is taken into account as a measure of controllability. We show that the proposed optimal placement strategy considerably outperforms heuristic methods including choosing hub nodes with high degree or betweenness centrality as drivers. We also study properties of optimal drivers in terms of various centrality measures including degree, betweenness, closeness, and clustering coefficient. The profile of these centrality values depends on the network structure. For homogeneous networks such as random small-world networks, the optimal driver nodes have almost the mean centrality value of the population (much lower than the centrality value of hub nodes), whereas the centrality value of optimal drivers in heterogeneous networks such as scale-free ones is much higher than the average and close to that of hub nodes. However, as the degree of heterogeneity decreases in such networks, the profile of centrality approaches the population mean.
控制网络结构在科学和工程领域有许多应用。在本文中，我们考虑了牵制控制问题（将动力学牵制到参考状态），并优化驱动节点（即输入控制信号的节点）的放置。考虑到局部可控性概念，基于拉普拉斯矩阵特征值的一个度量被用作可控性的一种度量。我们表明，所提出的最优放置策略显著优于启发式方法，包括选择具有高度或中介中心性的枢纽节点作为驱动节点。我们还根据包括度、中介性、接近性和聚类系数在内的各种中心性度量来研究最优驱动节点的性质。这些中心性值的分布取决于网络结构。对于诸如随机小世界网络这样的均匀网络，最优驱动节点几乎具有总体的平均中心性值（远低于枢纽节点的中心性值），而在诸如无标度网络这样的异质网络中，最优驱动节点的中心性值远高于平均值且接近枢纽节点的中心性值。然而，随着此类网络中异质性程度的降低，中心性分布趋近于总体平均值。
