在这篇文章中讨论了两个核心问题, 分别是最小输入问题和输入信号对节点的控制问题. 利用图论和矩阵理论, 找到了具有强控制集中性和强控制能力的最优的最小驱动节点集. 首先, 确定了驱动节点的最小数量. 然后, 通过两种方法确定了最优的最小驱动节点集, 一种是分析节点$i$ 的控制集中性, 另一种是查找控制信号$u^{+}(t)$和具有强控制能力的节点$i$ 之间有用的连接添加. 最后, 输入信号被施加到最优的最小驱动节点上以使得网络能控. 同时, 关于最优的最小驱动节点集的算法也被提出用于复杂网络能控性的研究.

Two core issues are studied in this paper, which are, respectively, the minimal number of input signals and how the input signal is injected to a controlled node to ensure complete controllability of a network. By taking advantage of graph and matrix theory, we focus on finding the optimal minimum driver nodes set with strong control centrality and strong control ability. Firstly, the minimum number of driver nodes is determined. Secondly, the optimal minimum driver nodes set is decided by two ways. One is analyzing the control centrality of node $i$, and the other is searching the optimal connection added between new control signal $u^{+}(t)$ and state node $i$ with strong control ability. Finally, the input signals are injected to the optimal minimum driver nodes to make the network controllable. Moreover, the algorithm of finding out the optimal minimum driver nodes set is also proposed for the controllability of complex networks.