复杂网络可控性问题的核心在于解决两个最少问题: 最 少需要多少输入和最少需要控制多少节点. Liu 和Barabasi 将现代 控制理论应用到线性系统的结构可控性问题上, 提出了最少需要多少输入 的计算方法, 解决了复杂有向网络结构能控性的可计算问题. 针对现实网 络中存在的无向图或者加权图, 文章引入了节点控制能力的概念, 利用添 加输入或者连边的方法, 给出了求系统精确可控的最小驱动点集合和极小被控点集合的算法.

In the controllability study of complex networks, there are basically two core issues: The minimal number of inputs and the minimal number of controlled nodes needed to achieve full control. Liu and Barabasi applied the modern control theory to the investigation of network structural controllability of linear dynamical systems and proposed a method to calculate the minimal number of inputs. This solves the computable problem of the complex network structural controllability. As to undirected or weighted networks in real networks, the paper introduces the concept of node control capacity for them. By using the method of adding inputs or edges, we propose algorithms to identify the minimal set of driver nodes as well as the approximately minimal set of controlled nodes to ensure the full control of network.