Adjacency-Based Spectral Proxy Control of Mobile Communication Agents

2026-08-12

AI Summary

This study addresses the challenge of distributedly estimating the Fiedler vector for algebraic connectivity control in mobile agent networks by proposing the A-Fiedler method. Replacing the Fiedler vector with the principal eigenvector of the adjacency matrix as a spectral proxy, this approach decomposes the gradient controller into local interactions and graph embeddings, enabling robust distributed online repositioning under communication constraints. Experimental results demonstrate that while A-Fiedler matches conventional methods in unconstrained settings, it significantly outperforms existing approaches in communication-limited scenarios. The method effectively prevents network disconnection and maintains system robustness, thereby establishing a novel paradigm for distributed connectivity maintenance in multi-agent systems.

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.

Problem

• Mobile Agent Network
• Algebraic Connectivity
• Fiedler Vector
• Distributed Estimation
• Real-time Control

Innovation

• A-Fiedler
• Adjacency Matrix Eigenvector
• Distributed Estimation
• Spectral Proxy Control
• Fiedler Gradient Decomposition