Achieving consensus via nearest neighbor rules is an important prerequisite for multi-agent networks to accomplish collective tasks. A common assumption in consensus setup is that each agent interacts with all its neighbors during the process. This paper examines whether network functionality and performance can be maintained-and even enhanced-when agents interact only with a subset of their respective (available) neighbors. As shown in the paper, the answer to this inquiry is affirmative. In this direction, we show that by using the monotonicity property of the Laplacian eigenvectors, a neighbor selection rule with guaranteed performance enhancements, can be realized for consensus-type networks. For the purpose of distributed implementation, a quantitative connection between Laplacian eigenvectors and the "relative rate of change" in the state between neighboring agents is further established; this connection facilitates a distributed algorithm for each agent to identify "favorable" neighbors to interact with. Multi-agent networks with and without external influence are examined, as well as extensions to signed networks. This paper underscores the utility of Laplacian eigenvectors in the context of distributed neighbor selection, providing novel insights into distributed data-driven control of multi-agent systems.

中文翻译：

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多代理网络中的分布式邻居选择

通过最近邻规则达成共识是多智能体网络完成集体任务的重要前提。共识设置中的一个常见假设是每个代理在此过程中与其所有邻居进行交互。本文研究了当代理仅与其各​​自（可用）邻居的子集交互时，是否可以保持甚至增强网络功能和性能。如论文所示，对这一询问的回答是肯定的。在这个方向上，我们表明，通过使用拉普拉斯特征向量的单调性，可以为共识型网络实现具有保证性能增强的邻居选择规则。为了分布式实现的目的，拉普拉斯特征向量和“相对变化率”之间的定量联系 在相邻代理之间的状态进一步建立；这种连接促进了每个代理的分布式算法，以识别与之交互的“有利”邻居。检查有和没有外部影响的多代理网络，以及对签名网络的扩展。本文强调了拉普拉斯特征向量在分布式邻居选择的背景下的实用性，为多代理系统的分布式数据驱动控制提供了新的见解。