多智能体系统中的簇分配
Cluster Assignment in Multi-Agent Systems
AI总结：
研究多智能体同质扩散网络的簇分配问题，通过设计有向图利用自同构群轨道保证系统收敛至预定簇配置，并给出所需边数的上下界及构造性生成方法。
摘要：
我们研究多智能体网络中的簇分配。我们考虑同质扩散网络，并专注于图的设计，以确保系统收敛到预定的簇配置，即指定簇的数量及每个簇中的智能体数量。利用簇合成的最新结果，我们证明可以设计一个有向图，使得该图的自同构群的作用具有预定大小的轨道，从而保证网络收敛到预定的簇配置。我们提供了构建这些图所需边数的上下界，以及生成这些图的构造性方法。我们用一些数值例子支持我们的分析。
英文摘要：
We study cluster assignment in multi-agent networks. We consider homogeneous diffusive networks, and focus on design of the graph that ensures the system will converge to a prescribed cluster configuration, i.e., specifying the number of clusters and agents within each cluster. Leveraging recent results from cluster synthesis, we show that it is possible to design an oriented graph such that the action of the automorphism group of the graph has orbits of predetermined sizes, guaranteeing that the network will converge to the prescribed cluster configuration. We provide upper and lower bounds on the number of edges that are needed to construct these graphs along with a constructive approach for generating these graphs. We support our analysis with some numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
