Adjacency-Based Spectral Proxy Control of Mobile Communication Agents

Abstract:We consider a heterogeneous mobile-agent network composed of uncontrolled task agents and controllable communication agents. The objective is to reposition communication agents online as task agents move. Since throughput-based objectives are generally unsuitable for real-time control, spectral graph metrics such as algebraic connectivity are commonly adopted as surrogate objectives. However, controlling algebraic connectivity relies on the eigenvector corresponding to the second-smallest eigenvalue of a graph's Laplacian matrix (i.e., the Fiedler vector), whose distributed estimation requires an unbounded number of communication rounds to converge. In this work, we identify a structural decomposition of this Fiedler-gradient controller into a local interaction rule and a graph embedding component, suggesting the use of alternative embeddings that are easier to estimate distributively than the Fiedler vector. As a particular instance, we propose A-Fiedler, which replaces the Fiedler embedding with the dominant eigenvector of the adjacency matrix, commonly used as a graph embedding of nodes into a latent geometry. This representation is more naturally suited for distributed implementation under local communication constraints. We evaluate A-Fiedler against the classical Fiedler-gradient controller. Results show comparable network performance in the absence of communication constraints and improved robustness under distributed estimation. For instance, under the same number of communication rounds, the Fielder-gradient may even converge to disconnected configurations whereas our proposition maintains performance. We believe our contribution provides a simpler path toward distributed network control.

Robotics (cs.RO); Machine Learning (cs.LG); Multiagent Systems (cs.MA); Systems and Control (eess.SY)

arXiv:2608.13616 [cs.RO]

(or arXiv:2608.13616v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2608.13616 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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