Topology Estimation for Open Multi-Agent Systems

Dimos V. Dimarogonas; Nana Wang; Pelin Sekercioglu

arxiv: 2604.13628 · v1 · submitted 2026-04-15 · 📡 eess.SY · cs.SY

Topology Estimation for Open Multi-Agent Systems

Nana Wang , Pelin Sekercioglu , Dimos V. Dimarogonas This is my paper

Pith reviewed 2026-05-10 13:21 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords topology estimationopen multi-agent systemsfast switchingleast-squares operatorsmode clusteringinteraction topologydissimilarity measure

0 comments

The pith

A projection-based dissimilarity measure from local least-squares consistency enables accurate topology estimation in fast-switching open multi-agent systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Open multi-agent systems have agents joining and leaving while their interactions switch on and off very quickly, leaving only brief intervals where any single topology holds. Standard segment-wise estimation and clustering methods become unreliable on these short segments because they lack enough data to detect patterns reliably. The paper derives a projection-based dissimilarity measure directly from the consistency property that local least-squares operators must satisfy when the underlying mode is the same. Intervals that produce similar operator behavior are clustered together, and data from all intervals inside one cluster are then aggregated to produce a single, accurate estimate of the interaction topology for that mode. This supplies a systematic way to reconstruct who interacts with whom even when the system changes too rapidly for conventional approaches.

Core claim

The paper establishes that a projection-based dissimilarity measure, obtained from the consistency property of local least-squares operators, permits robust clustering of short dwell-time intervals in open multi-agent systems subject to fast switching; once intervals are grouped by cluster, their data can be aggregated to recover accurate estimates of the underlying interaction topologies.

What carries the argument

The projection-based dissimilarity measure derived from the consistency property of local least-squares operators, which groups intervals by how similarly their local models behave.

If this is right

Accurate topology reconstruction becomes feasible for OMAS even when dwell times are too short for conventional segment-wise methods.
Aggregating data within each discovered cluster produces topology estimates that remain reliable under rapid node arrival and departure.
The same clustering step yields a complete reconstruction of all distinct interaction modes present during the observation window.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach may apply to any networked system whose structure switches faster than the data windows needed for ordinary identification.
Consistency of local estimators could serve as a general indicator for detecting structural changes in other linear or nonlinear time-varying networks.
Online implementations might allow real-time topology tracking in robotic teams or sensor networks that reconfigure frequently.

Load-bearing premise

The consistency property of local least-squares operators continues to hold for the short dwell-time intervals created by fast switching, and the resulting dissimilarity values separate distinct modes clearly enough for clustering to succeed.

What would settle it

Running the dissimilarity measure and clustering on recorded intervals from a controlled OMAS experiment whose true topologies are known in advance and observing that intervals from different known modes are grouped together or that same-mode intervals are split apart.

Figures

Figures reproduced from arXiv: 2604.13628 by Dimos V. Dimarogonas, Nana Wang, Pelin Sekercioglu.

**Figure 2.** Figure 2: The reference graphs for 8 agents and 10 agents [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: The evolution of the switching sequence with time. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: The evolution of the agent states with time. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Dendrogram for 8 agents showing the projection [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Dendrogram for 10 agents showing the projection [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

We address the problem of interaction topology identification in open multi-agent systems (OMAS) with dynamic node sets and fast switching interactions. In such systems, new agents join and interactions change rapidly, resulting in intervals with short dwell time and rendering conventional segment-wise estimation and clustering methods unreliable. To overcome this, we propose a projection-based dissimilarity measure derived from a consistency property of local least-squares operators, enabling robust mode clustering. Aggregating intervals within each cluster yields accurate topology estimates. The proposed framework offers a systematic solution for reconstructing the interaction topology of OMAS subject to fast switching. Finally, we illustrate our theoretical results via numerical simulations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a practical projection-based dissimilarity for clustering modes in fast-switching open MAS, but the full derivations and robustness checks are what would decide if it holds up.

read the letter

The main point is a new dissimilarity measure built from the consistency property of local least-squares operators. It is meant to let you cluster intervals reliably even when dwell times are short because agents join and leave and interactions flip quickly. By grouping those intervals and aggregating within clusters, the method produces topology estimates that standard segment-wise approaches cannot handle well in this setting. That construction is the actual novelty here, and it targets a concrete limitation in open multi-agent identification without relying on internal parameter fitting that could create circularity. The numerical simulations are presented as confirmation that the clustering succeeds under the stated conditions. The approach looks clean on the surface and avoids obvious internal contradictions. The soft spot is the load-bearing assumption that the consistency property survives the short intervals and any noise or model mismatch that comes with real open systems. Without seeing the explicit bounds, proof steps, or comparison against alternatives in the full text, it is hard to judge how much margin the method actually has. If those pieces are solid and the simulations include realistic switching rates, the work is useful. This is for control researchers who already work on networked identification and need a tool for the open, fast-switching case. A reader who cares about practical topology reconstruction in dynamic graphs would find the construction worth testing. I would send it to peer review because the problem is relevant and the idea is focused, even if the analysis sections will likely need tightening.

Referee Report

0 major / 3 minor

Summary. The paper addresses interaction topology identification in open multi-agent systems (OMAS) featuring dynamic node sets and fast-switching interactions that produce short dwell-time intervals. It introduces a projection-based dissimilarity measure derived from a consistency property of local least-squares operators to support robust mode clustering, followed by aggregation of intervals within each cluster to obtain accurate topology estimates. The framework is illustrated through numerical simulations.

Significance. If the consistency property of the local least-squares operators extends reliably to short dwell times, the approach could provide a useful systematic method for topology reconstruction in OMAS where conventional segment-wise estimation fails. The projection-based dissimilarity and clustering step represent a targeted response to the fast-switching challenge, with the simulations offering initial empirical support.

minor comments (3)

The abstract states that the consistency property enables robust clustering but does not specify the precise conditions (e.g., minimum dwell time or noise bounds) under which the property is guaranteed to hold; adding this would strengthen the claim.
No explicit statement is given on how the projection is constructed or normalized; a brief equation or definition in the main text would clarify the dissimilarity measure.
The numerical simulations are mentioned but lack details on the number of agents, switching rates, or performance metrics (e.g., topology error rates); including these would allow better assessment of practical utility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its potential significance in addressing topology identification under fast-switching interactions in open multi-agent systems. The referee's summary accurately captures the core contribution. No specific major comments were provided in the report, so we have no point-by-point revisions to discuss at this time. We remain available to provide additional details or clarifications should the referee have further questions.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives a projection-based dissimilarity measure from a stated consistency property of local least-squares operators to support mode clustering and topology aggregation in fast-switching OMAS. No equations, self-citations, or fitted parameters are provided that would allow any step to reduce by construction to its own inputs. The consistency property is treated as external rather than defined internally, and the clustering/aggregation steps follow from the measure without evident renaming, smuggling, or self-referential forcing. The derivation chain is therefore self-contained against the given description.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; the ledger is therefore minimal and provisional.

axioms (1)

domain assumption Local least-squares operators possess a consistency property that can be turned into a dissimilarity measure separating distinct interaction modes.
Invoked directly in the abstract as the foundation of the projection-based measure.

pith-pipeline@v0.9.0 · 5400 in / 1144 out tokens · 34475 ms · 2026-05-10T13:21:05.957917+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

Dimitrov, D., Sch¨ afer, P.S.L., Farr, E., Rodriguez-Mier, P., Lobentanzer, S., Badia-i Mompel, P., Dugourd, A., Tanevski, J., Ramirez Flores, R.O., and Saez-Rodriguez, J. (2024). Liana+ provides an all-in-one framework for cell–cell communication inference. Nature Cell Biology , 26(9), 1613–1622. Franceschelli, M. and Frasca, P. (2020). Stability of open...

work page 2024
[2]

Kaufman, L

PTR Prentice-Hall Upper Saddle River, NJ. Kaufman, L. and Rousseeuw, P.J. (2009). Finding groups in data: an introduction to cluster analysis . John Wiley & Sons. Massucci, L., Lauer, F., and Gilson, M. (2021). Regular- ized switched system identiﬁcation: a statistical learning perspective. IF AC-PapersOnLine, 54(5), 55–60. Massucci, L., Lauer, F., and Gi...

work page 2009
[3]

Restrepo, E., Lor ´ ıa, A., Sarras, I., and Marzat, J. (2022). Consensus of open multi-agent systems over dynamic undirected graphs with preserved connectivity and col- lision avoidance. In Proc. IEEE CDC , 4609–4614. Rey, S., Das, B., and Isuﬁ, E. (2025). Online learning of expanding graphs. IEEE Open Journal of Signal Processing. S ¸ekercio˘ glu, P., Fo...

work page 2022

[1] [1]

Dimitrov, D., Sch¨ afer, P.S.L., Farr, E., Rodriguez-Mier, P., Lobentanzer, S., Badia-i Mompel, P., Dugourd, A., Tanevski, J., Ramirez Flores, R.O., and Saez-Rodriguez, J. (2024). Liana+ provides an all-in-one framework for cell–cell communication inference. Nature Cell Biology , 26(9), 1613–1622. Franceschelli, M. and Frasca, P. (2020). Stability of open...

work page 2024

[2] [2]

Kaufman, L

PTR Prentice-Hall Upper Saddle River, NJ. Kaufman, L. and Rousseeuw, P.J. (2009). Finding groups in data: an introduction to cluster analysis . John Wiley & Sons. Massucci, L., Lauer, F., and Gilson, M. (2021). Regular- ized switched system identiﬁcation: a statistical learning perspective. IF AC-PapersOnLine, 54(5), 55–60. Massucci, L., Lauer, F., and Gi...

work page 2009

[3] [3]

Restrepo, E., Lor ´ ıa, A., Sarras, I., and Marzat, J. (2022). Consensus of open multi-agent systems over dynamic undirected graphs with preserved connectivity and col- lision avoidance. In Proc. IEEE CDC , 4609–4614. Rey, S., Das, B., and Isuﬁ, E. (2025). Online learning of expanding graphs. IEEE Open Journal of Signal Processing. S ¸ekercio˘ glu, P., Fo...

work page 2022