Establishing the graph-based criterion for the selection of any location and any number of leaders is the main difficulty in the complete graphic characterization of multiagent controllability. This greatly increases the complexity of the study, compared with the results derived for only one or several classes of leaders. Through a detailed analysis of graphs of six nodes, this article presents a systematic design and identification process for the complete graphic characterization by taking advantage of controllability destructive nodes. The topologies obtained by the proposed method allow directly determining controllability at the network topology level. The results are not only applicable to any leader's selection but also reveal the difficulty and complexity in the study of complete controllability graphic characterizations. Moreover, by comparing graphs composed of five and six nodes, the results reveal the graph-theory-based controllability complexity caused by adding only one node. Finally, results are derived to show how to design topology structures to ensure the controllability under any selection of leaders.

中文翻译：

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多智能体可控性的完整图形表征的复杂性


建立基于图的标准来选择任何位置和任意数量的领导者是多智能体可控性的完整图形表征的主要困难。与仅针对一类或几类领导者得出的结果相比，这大大增加了研究的复杂性。通过对六个节点图的详细分析，提出了利用可控性破坏节点进行完整图形表征的系统设计和识别过程。通过所提出的方法获得的拓扑允许直接确定网络拓扑级别的可控性。结果不仅适用于任何领导者的选择，而且揭示了完全可控性图形表征研究的难度和复杂性。此外，通过比较由5个和6个节点组成的图，结果揭示了仅添加一个节点所带来的基于图论的可控复杂性。最后，得出的结果表明如何设计拓扑结构以确保在任何领导者选择下的可控性。