提升pinning同步性速度：高反馈增益的低度节点
Enhancing speed of pinning synchronizability: low-degree nodes with high feedback gains
AI总结：
本文提出通过限制控制成本，建立与pinning可控性速度相关的线性矩阵不等式，发现低度节点可获得高反馈增益，从而提升系统控制速度。
摘要：
控制复杂网络在科学和工程中至关重要。尽管近期努力提升可控性和同步强度，但pinning同步性速度（pinning控制的收敛速率）及相应pinning节点选择却鲜受关注。为此，我们提出假设以限制控制成本，建立与pinning可控性速度相关的线性矩阵不等式。通过求解不等式，我们获得所有节点的pinning可控性速度及最优控制强度（pinning控制中的反馈增益）。有趣的是，某些低度节点能够实现较大的反馈增益，表明它们对控制系统有重要影响。此外，当选择具有高反馈增益的节点作为pinning节点时，实际系统的控制速度显著高于传统大度和大介数选择。因此，所提方法为研究pinning可控性速度提供了新途径，并可激发其他有效的启发式pinning节点选择方法用于大规模系统。
英文摘要：
Controlling complex networks is of paramount importance in science and engineering. Despite recent efforts to improve controllability and synchronous strength, little attention has been paid to the speed of pinning synchronizability (rate of convergence in pinning control) and the corresponding pinning node selection. To address this issue, we propose a hypothesis to restrict the control cost, then build a linear matrix inequality related to the speed of pinning controllability. By solving the inequality, we obtain both the speed of pinning controllability and optimal control strength (feedback gains in pinning control) for all nodes. Interestingly, some low-degree nodes are able to achieve large feedback gains, which suggests that they have high influence on controlling system. In addition, when choosing nodes with high feedback gains as pinning nodes, the controlling speed of real systems is remarkably enhanced compared to that of traditional large-degree and large-betweenness selections. Thus, the proposed approach provides a novel way to investigate the speed of pinning controllability and can evoke other effective heuristic pinning node selections for large-scale systems.
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