Distributed Neighbor Selection in Multiagent Networks

Achieving consensus via nearest neighbor rules is an important prerequisite for multiagent networks to accomplish collective tasks. A common assumption in consensus setup is that each agent interacts with all its neighbors. This article 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 this article, the answer to this inquiry is affirmative. In this direction, we show that by exploring the monotonicity property of the Laplacian eigenvectors, a neighbor selection rule with guaranteed performance enhancements can be realized for consensus-type networks. For distributed implementation, a quantitative connection between entries of 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. Multiagent networks with and without external influence are examined, as well as extensions to signed networks. This article underscores the utility of Laplacian eigenvectors in the context of distributed neighbor selection, providing novel insights into distributed data-driven control of multiagent systems.