cs.ROAug 12, 2026

Adjacency-Based Spectral Proxy Control of Mobile Communication Agents

Authors: Mariana del Castillo, Federico Larroca

Organizations: Facultad de Ingenier´ıa Universidad de la Rep´ublica Montevideo, Uruguay

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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.

Figures & tables

 N=5N=5N=8N=8N=10N=10
MethodDisc.MNFConv.Disc.MNFConv.Disc.MNFConv.
 (%)(%) ±\pm SDiter.(%)(%) ±\pm SDiter.(%)(%) ±\pm SDiter.
A_exact0.0+10.5±9.1+10.5\pm 9.162.70.0+5.4±5.6+5.4\pm 5.673.80.0+0.7±3.2+0.7\pm 3.280.8
L_exact0.0+16.1±6.5+16.1\pm 6.553.00.0+7.0±5.1+7.0\pm 5.170.60.0+1.7±2.7+1.7\pm 2.780.3
A_dist0.0+10.5±9.1+10.5\pm 9.162.70.0+5.4±5.6+5.4\pm 5.674.00.0+0.7±3.2+0.7\pm 3.280.8
L_dist95.0−320.6±131.0-320.6\pm 131.081.515.0−31.7±86.1-31.7\pm 86.160.520.0−25.9±62.4-25.9\pm 62.476.7
TABLE I: Performance comparison for different network sizes. Relative MNF change and convergence statistics are averaged over 20 realizations.
Fig. 1: Dynamic tracking experiment comparing the four methods. Top: communication-agent repositioning while task agents follow a clover-shaped trajectory. Bottom: relative MNF evolution over time. The highlighted window indicates the time interval corresponding to the bold trajectory segments shown in the top panels.
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