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Scaled Group Consensus over Weakly Connected Structurally Balanced Graphs

机译：缩放组在结构平衡的图形弱连接​​方面共识

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摘要

A graph Laplacian based distributed protocol that can achieve a group consensus over weighted, signed, directed, and weakly connected graphs is investigated. It is said to achieve the group consensus if the state of agents who belong to the same group converges to a common value, while the one of agents who belong to another group converges to a different value. It is assumed that no agent knows which group she belongs to before the protocol is executed. In this paper, for a given signed graph which contains a directed spanning tree, namely, at least one leader that can affect all of the other agents, a definition of n-structurally balanced is proposed. It is emphasized that this definition is a generalization of the structurally balanced which leads a bipartite consensus. Then, necessary and sufficient conditions are established to guarantee the agents’ state reaching the group consensus. The results are illustrated through numerical examples.
机译：研究了基于Laplacian的分布式协议，可以研究加权，签名，指导和弱连接图的组共识。据说如果属于同一组的代理人会聚到共同值的代理人，则达成本集团的共识，而属于另一个组的代理人则会聚到不同的价值。假设没有代理人知道在执行协议之前属于哪个群体。在本文中，对于包含定向生成树的给定符号图，即，提出了可以影响所有其他代理的至少一个领导者，提出了n结构平衡的定义。强调，该定义是结构平衡的概括，其引导二分支共识。然后，建立必要和充分的条件，以保证代理商达成本集团共识的国家。结果通过数值例子说明。

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