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arxiv: 2605.23356 · v1 · pith:KVHQSJZUnew · submitted 2026-05-22 · 📡 eess.SY · cs.SY

A Distributed Framework for Data-Driven Safe Coordination in Leader-Follower Networks

Mirhan Urkmez , Maryam Sharifi , Shahab Heshmati-Alamdari This is my paper

Pith reviewed 2026-05-25 03:52 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords data-driven controlcontrol barrier functionsmulti-agent systemsleader-follower networksconnectivity preservationsafe coordinationzeroing control barrier functionsdistributed control
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The pith

Data-derived bounds from local inputs suffice to keep leader-follower networks connected without knowing agent dynamics.

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

The paper develops a distributed framework that preserves connectivity in leader-follower multi-agent systems whose dynamics are unknown and only local state information is available. It introduces the 3D-ZCBF approach to find derivative bounds directly from collected input-state data so that safety sets remain invariant without building explicit high-dimensional models. Individual safety conditions for leader-leader, follower-follower, and leader-follower pairs are written in decoupled form and then aggregated into explicit system-wide requirements that guarantee the full communication network stays intact. The work also quantifies how data-set size and bound accuracy affect whether those safety certificates remain feasible. A projection-based controller implements the conditions and uses only two-hop local information.

Core claim

The 3D-ZCBF framework ensures the controlled invariance of safety sets by identifying derivative bounds from input-state data without requiring explicit models of high-dimensional agent dynamics, derives explicit decoupled safety conditions for leader-leader and follower-follower pairings, aggregates those conditions together with leader-follower constraints into system-wide conditions that formally guarantee preservation of the entire communication network, and supplies a quantitative analysis of how data-set size and learned Jacobian bound accuracy affect certificate feasibility.

What carries the argument

The distributed data-driven zeroing control barrier function (3D-ZCBF) that identifies derivative bounds from input-state data to enforce controlled invariance of safety sets.

If this is right

  • Connectivity preservation reduces to a set of explicit, decoupled local conditions that can be checked with only two-hop information.
  • The same data-driven bounds simultaneously handle leader-leader, follower-follower, and leader-follower pairings.
  • Feasibility of the safety certificates improves monotonically with larger data sets and tighter bound accuracy.
  • A single projection-based controller can enforce all aggregated conditions in real time.

Where Pith is reading between the lines

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

  • The same data-to-bound pipeline could be reused for other local safety specifications beyond connectivity, such as collision avoidance.
  • If the quantitative feasibility curves hold, practitioners can decide in advance how much data to collect before deployment.
  • The decoupling of pairwise conditions suggests the framework may scale to larger networks without combinatorial explosion in the number of constraints.

Load-bearing premise

The collected input-state data set must be large enough and of sufficient quality to produce Jacobian and derivative bounds accurate enough that the resulting safety certificates remain feasible.

What would settle it

Apply the projection-based controller using the data-derived bounds on a physical leader-follower network and check whether any communication link is lost while the explicit system-wide conditions are still satisfied.

Figures

Figures reproduced from arXiv: 2605.23356 by Maryam Sharifi, Mirhan Urkmez, Shahab Heshmati-Alamdari.

Figure 1
Figure 1. Figure 1: Geometric decomposition used in the follower–follower [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Simulation results for 1-Dimensional leader–follower system [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Simulation results for 2-Dimensional leader–follower system [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Representative control input trajectories for datasets gener [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
read the original abstract

This paper addresses connectivity preservation in leader-follower multi-agent systems with unknown control-affine dynamics and local state information. We introduce the distributed data-driven zeroing control barrier function (3D-ZCBF) framework, which ensures the controlled invariance of safety sets by identifying derivative bounds from input-state data without requiring explicit models of high-dimensional agent dynamics. In this work, we derive the explicit, decoupled safety conditions necessary to maintain connectivity for leader-leader, and follower-follower pairings. These individual constraints, along with the leader-follower conditions, are aggregated into explicit system-wide conditions that formally guarantee the preservation of the entire communication network. Furthermore, we provide a quantitative analysis demonstrating how the size of the collected data set and the accuracy of the learned Jacobian bounds impact the feasibility of the safety certificates. The proposed conditions are implemented via a projection-based controller, and simulations confirm that these explicit 3D-ZCBF requirements effectively maintain system-level connectivity using only local, two-hop information.

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.

Referee Report

2 major / 2 minor

Summary. The paper introduces the distributed data-driven zeroing control barrier function (3D-ZCBF) framework for connectivity preservation in leader-follower multi-agent systems with unknown control-affine dynamics. It identifies derivative bounds from input-state data to derive explicit decoupled safety conditions for leader-leader, follower-follower, and leader-follower pairings, aggregates these into system-wide conditions guaranteeing network preservation, implements them via a projection-based controller using local two-hop information, and includes quantitative analysis of data-set size and Jacobian-bound accuracy on certificate feasibility, with simulation validation.

Significance. If the central claims hold, the work offers a meaningful advance in model-free safe coordination for high-dimensional multi-agent systems by converting data into formal controlled-invariance certificates without explicit dynamics. The explicit aggregation of per-pair conditions and the quantitative study of data requirements are strengths that could support practical deployment in robotics and networked control where models are unavailable.

major comments (2)
  1. [quantitative analysis section] The quantitative analysis section: while it illustrates how data-set size and bound accuracy affect feasibility of the safety certificates, it does not supply a concrete result (theorem, bound, or scaling law) establishing that there exists a finite data volume yielding sufficiently tight Jacobian/derivative bounds to keep the aggregated 3D-ZCBF conditions feasible for the true unknown dynamics in high-dimensional regimes. This is load-bearing for the claim that formal system-wide guarantees are realized in practice from collected data.
  2. [§4] §4 (derivation of decoupled conditions): the reduction from the data-driven bounds to the per-pair 3D-ZCBF inequalities is presented, but the manuscript does not explicitly verify that these inequalities recover the standard model-based ZCBF conditions in the limit of perfect data (i.e., exact Jacobian), which would strengthen the consistency of the data-driven extension.
minor comments (2)
  1. [simulation section] The simulation section would benefit from an explicit statement of the numerical values used for the projection operator and the data-collection protocol (number of samples per agent, excitation signal).
  2. [Table 1] Table 1 (or equivalent): the reported feasibility percentages for varying data sizes should include confidence intervals or standard deviations across repeated trials to allow assessment of variability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and positive review. We address each major comment below with point-by-point responses.

read point-by-point responses

  1. Referee: [quantitative analysis section] The quantitative analysis section: while it illustrates how data-set size and bound accuracy affect feasibility of the safety certificates, it does not supply a concrete result (theorem, bound, or scaling law) establishing that there exists a finite data volume yielding sufficiently tight Jacobian/derivative bounds to keep the aggregated 3D-ZCBF conditions feasible for the true unknown dynamics in high-dimensional regimes. This is load-bearing for the claim that formal system-wide guarantees are realized in practice from collected data.

    Authors: We agree that the quantitative analysis provides empirical demonstration of the effects of data-set size and bound accuracy but does not include a general theorem, bound, or scaling law guaranteeing that a finite data volume suffices to produce sufficiently tight bounds for feasibility in arbitrary high-dimensional regimes. Deriving such a result would require additional assumptions on the unknown dynamics or sampling that lie outside the present framework. The section instead supplies practical guidance on how these factors influence certificate feasibility, corroborated by the simulation results. We will revise the text to explicitly delineate the scope of the provided guarantees and identify the absence of a general existence result as an avenue for future investigation. revision: partial

  2. Referee: §4 (derivation of decoupled conditions): the reduction from the data-driven bounds to the per-pair 3D-ZCBF inequalities is presented, but the manuscript does not explicitly verify that these inequalities recover the standard model-based ZCBF conditions in the limit of perfect data (i.e., exact Jacobian), which would strengthen the consistency of the data-driven extension.

    Authors: We appreciate this observation. When the data-driven Jacobian bounds converge to the exact Jacobian (i.e., in the limit of perfect data), the derived per-pair 3D-ZCBF inequalities reduce directly to the classical model-based ZCBF conditions for connectivity preservation. We will add a concise remark or short proposition in Section 4 that explicitly verifies this limiting case to reinforce the consistency of the data-driven formulation. revision: yes

Circularity Check

0 steps flagged

No circularity: data-driven bounds feed explicit, non-tautological safety conditions

full rationale

The derivation collects input-state data to obtain Jacobian/derivative bounds, then algebraically produces decoupled per-pair 3D-ZCBF conditions that are aggregated into system-wide certificates. These steps are forward derivations from the identified bounds; the quantitative feasibility analysis is an independent sensitivity result rather than a re-statement of the invariance claim. No self-definitional loops, fitted quantities renamed as predictions, or load-bearing self-citations appear in the provided description. The chain remains self-contained against external data and the standard ZCBF invariance theorem.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no specific free parameters, axioms, or invented entities can be identified from the provided information.

pith-pipeline@v0.9.0 · 5707 in / 1124 out tokens · 23062 ms · 2026-05-25T03:52:48.679354+00:00 · methodology

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