REVIEW 3 minor 20 references
Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs
T0 review · 0 major / 3 minor · reviewed 2026-05-25 · grok-4.3
Pith's one-line read Agents in time-varying graphs can resiliently track arbitrary reference states from leaders despite adversarial agents.
desk verdict The paper extends resilient consensus to let normal agents track arbitrary leader references outside the convex hull in time-varying graphs despite bounded adversaries. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
Resilient update rules for discrete-time leader-follower consensus in time-varying graphs that filter adversarial influences while tracking external references.
What would settle it
A simulation or experiment where the number of adversaries exceeds the bound and normal agents fail to track the reference state.
Extended reading notes
Core claim
There exist resilient update rules allowing normally behaving agents to track the reference state propagated by leaders in time-varying graphs, even when a bounded subset of leaders and followers are adversarial, provided the graphs satisfy sufficient connectivity over bounded time intervals.
Load-bearing premise
The communication graphs must be sufficiently connected over bounded time intervals and the number of adversarial agents must stay below the tolerance of the update rules.
Editorial extensions
If this is right
- Normal agents achieve consensus to reference values outside the convex hull of their initial states.
- The approach works for time-varying graphs under periodic connectivity conditions.
- Adversarial behavior is tolerated as long as it is below a known bound.
- Simulations confirm the tracking performance under the stated conditions.
Reading between the lines
- These rules could be tested in physical robot teams with wireless communication that changes over time.
- If the adversary bound is violated, tracking may diverge from the reference.
- Extensions might include handling delays or continuous-time dynamics.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript proposes methods for resilient leader-follower consensus in time-varying directed graphs under discrete-time dynamics. Normal agents track an arbitrary reference state propagated by a set of leaders, despite a bounded number F of adversarial agents among both leaders and followers, by applying filtering-based update rules (variants of W-MSR) under (r+1)-robustness conditions on the union of the graphs over bounded time intervals.
Significance. If the stated guarantees hold, the work usefully extends resilient consensus results (which confine the value to the convex hull of initial normal states) to a leader-follower tracking setting with arbitrary references. This is relevant for applications such as formation control or state tracking in adversarial multi-agent networks. The reliance on standard robustness assumptions and the inclusion of simulation validation are positive features.
minor comments (3)
- [Abstract] Abstract: the phrase 'bounded subset of the leaders and followers behaving adversarially' should explicitly relate the bound F to the robustness parameter r of the graph condition (e.g., r > F) to make the prerequisite assumptions immediately clear to readers.
- [Introduction] The manuscript would benefit from a brief comparison paragraph in the introduction or related-work section that distinguishes the new leader-follower tracking result from prior resilient consensus papers that only achieve convex-hull consensus.
- [Simulations] Simulation section: the figures should include explicit labels for the time-varying graph sequence, the value of F, and the robustness parameter used, so that readers can directly map the plots to the stated theorem assumptions.
Simulated Author's Rebuttal
We thank the referee for the positive assessment of our work on resilient leader-follower consensus in time-varying graphs and for recommending minor revision. No specific major comments were provided in the report.
Circularity Check
No significant circularity; derivation is self-contained
full rationale
The paper extends standard resilient consensus methods (variants of W-MSR) to a leader-follower setting for tracking arbitrary references in time-varying graphs. The central claims rest on explicit, externally stated assumptions about (r+1)-robustness of graph unions over bounded intervals and a known adversary bound F, which are prerequisites rather than outputs. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the result to its own inputs appear in the abstract or framing. The derivation chain is independent of the target result and relies on prior literature as external support.
Assumptions & free parameters
Cite this review
Pith. "Pith review of Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs." pith.science (2026). https://pith.science/paper/MVWXV7CA
@misc{pith2026190609096,
author = {Pith},
title = {Pith review of: Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs},
year = {2026},
howpublished = {\url{https://pith.science/paper/MVWXV7CA}},
note = {Machine review of arXiv:1906.09096}
}
read the original abstract
Several algorithms in prior literature have been proposed which guarantee consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the convex hull of initial normal agents' states, with the exact consensus value possibly being unknown. In leader-follower consensus problems however, the objective is for normally behaving agents to track a reference state that may take on values outside of this convex hull. In this paper we present methods for agents in time-varying graphs with discrete-time dynamics to resiliently track a reference state propagated by a set of leaders despite a bounded subset of the leaders and followers behaving adversarially. Our results are demonstrated through simulations.
Figures
Reference graph
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Reviewed May 25, 2026 · model on record in the stance chip above.
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