多智能体系统的信息交换图中存在自同构时, 系统可控性随领 导者选取的不同而不同, 针对这一情况, 文章利用图论的研究方法, 将自同 构与领导者对称的关系重新总结和定义, 提出了系统不可控的条件. 在此基础上进一步提出了在一种特殊拓扑结构中使系统不可控的领导者选择的方法, 从等价划分和几乎等价划分两方面分析不可控的情况, 从而排除了拓扑结构中大量不能控的领导者选择情形. 此外, 论述了只有自同构存在才能使系统不可控的条件. 该研究为含有自同构的拓扑结构复杂图判断可控性提供了方法.

When there is automorphism in the information exchange graph of multi-agent system, the controllability of the system varies with the leader's choice. In view of this situation, this paper uses the method of graph theory to re-summarize and define the relationship between automorphism and leader's symmetry, and puts forward the conditions for the system to be uncontrollable. On this basis, it further proposes the conditions for the system to be uncontrollable in a special topological structure. The method of leader selection analyses the uncontrollable situation from two aspects of equitable partitions and almost equitable partitions, thus, eliminating a large number of uncontrollable leader selection cases in the topological structure. In addition, the condition that only the existence of automorphism can make the system uncontrollable is discussed. This study provides a method for judging the controllability of complex graph with automorphism.