Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs

Dimitra Panagou; James Usevitch

arxiv: 1906.09096 · v1 · pith:MVWXV7CAnew · submitted 2019-06-19 · 📡 eess.SY · cs.SY

Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs

James Usevitch , Dimitra Panagou This is my paper

Pith reviewed 2026-05-25 19:55 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords resilient consensusleader-follower consensustime-varying graphsadversarial agentsmulti-agent systemsdiscrete-time dynamicsreference tracking

0 comments

The pith

Agents in time-varying graphs can resiliently track arbitrary reference states from leaders despite adversarial agents.

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

The paper presents methods for multi-agent systems with discrete-time dynamics operating over time-varying graphs to achieve resilient leader-follower consensus. Normal agents track a reference state set by leaders, even when some leaders and followers are adversarial, as long as their number is bounded. This extends previous resilient consensus algorithms that only guarantee values inside the convex hull of initial normal states. A reader would care because it enables reliable tracking of external commands in networks that may have faults or attacks and changing connections.

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.

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.

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.

Where Pith is reading between the lines

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

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.

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.

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.

Figures

Figures reproduced from arXiv: 1906.09096 by Dimitra Panagou, James Usevitch.

**Figure 3.** Figure 3: Leader-follower simulation using the SW-MSR algorithm with a [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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.

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 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 main takeaway is that this work moves resilient consensus past the convex-hull limit so that a set of leaders can drive the group to any chosen reference while normal followers still filter adversarial inputs. The setting is discrete-time agents on switching graphs, with a known bound F on total adversaries among both leaders and followers. They rely on standard filtering rules (variants of W-MSR) plus (r+1)-robustness conditions on the union graph over bounded intervals, which is the usual way to guarantee connectivity in time-varying networks. Simulations are included to show convergence to the reference under attack. That combination is the actual new piece; prior resilient results stopped at agreement inside the hull, and leader-follower papers usually assumed no adversaries. The extension is straightforward once the pieces are put together, but it fills a gap that matters for applications where the target is set externally rather than emerging from the agents themselves. The assumptions stay explicit and standard—no hidden circularity or invented entities. The main soft spot is that the abstract gives no proof sketches or exact robustness parameters, so it is hard to judge how conservative the interval-connectivity requirement ends up being or whether the bound F must be known very precisely. If the full proofs hold without extra restrictions, the result is solid for the subfield. This is for people already working on resilient multi-agent coordination or secure leader-follower control; a reader outside that niche will not get much from it. It is worth sending to referees because the claim is clear, the gap is real, and the simulations line up with the stated assumptions.

Referee Report

0 major / 3 minor

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

0 responses · 0 unresolved

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

0 steps flagged

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.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; assessment limited to the high-level description of bounded adversaries and time-varying graphs.

pith-pipeline@v0.9.0 · 5644 in / 973 out tokens · 39251 ms · 2026-05-25T19:55:45.839914+00:00 · methodology

discussion (0)

Reference graph

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S. M. Dibaji, H. Ishii, and R. Tempo, “Resilient randomized quantized consensus,” IEEE Transactions on Automatic Control , vol. 63, no. 8, pp. 2508–2522, 2018

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A. Mitra and S. Sundaram, “Secure distributed observers for a class of linear time invariant systems in the presence of Byzantine adversaries,” in Decision and Control (CDC), 2016 IEEE 55th Conference on . IEEE, 2016, pp. 2709–2714

work page 2016

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work page internal anchor Pith review Pith/arXiv arXiv 2018

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J. Usevitch and D. Panagou, “Resilient leader-follower consensus to arbitrary reference values,” in 2018 Annual American Control Conference (ACC). IEEE, 2018, pp. 1292–1298

work page 2018

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Secure distributed state estimation of an lti system over time-varying networks and analog erasure channels,

A. Mitra and S. Sundaram, “Secure distributed state estimation of an lti system over time-varying networks and analog erasure channels,” in 2018 Annual American Control Conference (ACC) . IEEE, 2018, pp. 6578–6583

work page 2018

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C.-Y . Koo, V . Bhandari, J. Katz, and N. H. Vaidya, “Reliable broadcast in radio networks: The bounded collision case,” in Proceedings of the twenty-ﬁfth annual ACM symposium on Principles of distributed computing. ACM, 2006, pp. 258–264

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H. J. LeBlanc and X. D. Koutsoukos, “Algorithms for determining network robustness,” in Proceedings of the 2nd ACM international conference on High conﬁdence networked systems . ACM, 2013, pp. 57–64

work page 2013

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Determining r-robustness of digraphs using mixed integer linear programming,

J. Usevitch and D. Panagou, “Determining r-robustness of digraphs using mixed integer linear programming,” in 2019 Annual American Control Conference (ACC), to appear . IEEE, 2019

work page 2019

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Determining r-and (r, s)-robustness of digraphs using mixed integer linear programming,

——, “Determining r-and (r, s)-robustness of digraphs using mixed integer linear programming,” arXiv preprint arXiv:1901.11000 , 2019

work page arXiv 1901

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r-robustness and (r, s)-robustness of circulant graphs,

——, “r-robustness and (r, s)-robustness of circulant graphs,” in 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017, pp. 4416–4421

work page 2017

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Circulants and their connectivities,

F. Boesch and R. Tindell, “Circulants and their connectivities,” Journal of Graph Theory , vol. 8, no. 4, pp. 487–499, 1984

work page 1984

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Graphs with circulant adjacency matrices,

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work page 1970