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arxiv: 1906.08254 · v1 · pith:JHTJHW45new · submitted 2019-06-19 · 📡 eess.SY · cs.SY

Resilient Leader-Follower Consensus with Time-Varying Leaders in Discrete-Time Systems

James Usevitch , Dimitra Panagou This is my paper

Pith reviewed 2026-05-25 20:00 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords resilient consensusleader-follower consensusdiscrete-time systemsadversarial agentstime-varying referencemulti-agent systemsfault tolerance
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The pith

Discrete-time agents can track time-varying leader references resiliently despite bounded adversarial leaders and followers.

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

Standard resilient consensus keeps values inside the convex hull of normal agents' initial states, but leader-follower problems require normal agents to follow an external time-varying reference that can lie outside that hull. This paper presents a method for agents obeying discrete-time dynamics to achieve that tracking when only a bounded subset of leaders and followers behave adversarially. The method works when the communication graph permits resilient information exchange under the given bound on adversaries. Simulations confirm that normal agents maintain tracking in the presence of the allowed number of adversarial agents.

Core claim

The authors present a method for agents with discrete-time dynamics to resiliently track a set of leaders' common time-varying reference state despite a bounded subset of the leaders and followers behaving adversarially.

What carries the argument

Resilient leader-follower tracking algorithm for discrete-time dynamics that filters adversarial influences using graph connectivity.

If this is right

  • Normal agents achieve asymptotic tracking of the time-varying reference.
  • The achieved state is permitted to lie outside the convex hull of initial normal states.
  • The guarantee holds only when the number of adversarial leaders and followers remains within the assumed bound.
  • Simulations demonstrate successful tracking under the stated conditions.

Where Pith is reading between the lines

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

  • The same filtering approach could be tested on graphs with varying degrees of connectivity to identify the minimal resilience threshold.
  • Extension to agents with continuous-time dynamics would require checking whether the discrete-time filtering steps carry over directly.
  • The method connects to problems of secure coordination in networks where external references must be followed under attack.

Load-bearing premise

Only a bounded number of agents behave adversarially and the communication graph permits resilient information exchange under that bound.

What would settle it

A network simulation in which the number of adversarial agents exceeds the bound and normal agents lose the ability to track the leaders' reference state.

Figures

Figures reproduced from arXiv: 1906.08254 by Dimitra Panagou, James Usevitch.

Figure 1
Figure 1. Figure 1: Demonstration of the MS-RPA algorithm. Leader agents’ states are [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
read the original abstract

The problem of consensus in the presence of adversarially behaving agents has been studied extensively in the literature. The proposed algorithms typically guarantee that the consensus value lies within the convex hull of initial normal agents' states. In leader-follower consensus problems however, the objective for normally behaving agents is to track a time-varying reference state that may take on values outside of this convex hull. In this paper we present a method for agents with discrete-time dynamics to resiliently track a set of leaders' common time-varying reference state despite a bounded subset of the leaders and followers behaving adversarially. The efficacy of 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.

Referee Report

1 major / 2 minor

Summary. The manuscript presents a distributed update rule for discrete-time multi-agent systems that enables normal agents to asymptotically track a common time-varying reference state injected by normal leaders, despite up to F adversarial leaders and followers. The algorithm combines local state feedback with a resilient averaging step that discards the F largest and F smallest neighbor values; the underlying directed graph is assumed to be (F+1,F+1)-robust. The central argument shows that the tracking error contracts under this robustness condition, relaxing the usual convex-hull containment property via leader injection. Efficacy is illustrated by simulations.

Significance. If the derivation holds, the result is a useful extension of resilient consensus to the leader-follower setting with exogenous time-varying signals. Standard (F+1,F+1)-robustness is preserved while accommodating linear dynamics and references outside the initial convex hull; the contraction argument for tracking error is a clear technical contribution. The work supplies a concrete, distributed protocol rather than an existence result only.

major comments (1)
  1. [Main theorem / tracking-error analysis] The proof that the tracking error contracts (presumably in the main theorem) must explicitly bound the contribution of the reference's time derivative; without a uniform bound on the rate of change of the leaders' common reference, asymptotic tracking need not hold for arbitrary time variation.
minor comments (2)
  1. [Abstract and simulation section] The abstract states that simulations demonstrate efficacy but supplies no quantitative metrics (e.g., steady-state error, convergence time) or comparison against non-resilient baselines; these should be added to the simulation section for clarity.
  2. [Algorithm description] Notation for the resilient averaging operator and the state-feedback gain should be introduced once and used consistently; currently the description mixes “resilient averaging term” with the update equation without a single defining expression.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thoughtful review and the specific comment on the tracking-error analysis. We address the point directly below.

read point-by-point responses

  1. Referee: [Main theorem / tracking-error analysis] The proof that the tracking error contracts (presumably in the main theorem) must explicitly bound the contribution of the reference's time derivative; without a uniform bound on the rate of change of the leaders' common reference, asymptotic tracking need not hold for arbitrary time variation.

    Authors: We agree that an explicit uniform bound on the rate of change of the reference is required for the contraction argument to hold under arbitrary time variation. In the revised manuscript we will add the standing assumption that the leaders' common reference satisfies ||r(k+1)-r(k)|| ≤ δ for a known constant δ ≥ 0. We will then insert this bound explicitly into the tracking-error recursion in the proof of the main theorem, showing that the error still contracts to a neighborhood whose size depends on δ (and vanishes when δ=0). The theorem statement and all subsequent claims will be updated accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper adapts standard resilient consensus techniques (discarding F extreme values under (F+1,F+1)-robustness) to discrete-time leader-follower tracking of a time-varying reference. The central argument shows contraction of the tracking error for normal agents via the graph robustness assumption and bounded adversaries; this does not reduce to a fitted parameter, self-definition, or load-bearing self-citation chain. The convex-hull relaxation is explicitly handled by leader injection, and the proof proceeds from first principles under the stated connectivity conditions. Simulations are illustrative only. No step equates a prediction to its input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the work implicitly relies on standard multi-agent assumptions such as bounded adversaries and suitable graph connectivity that are not detailed here.

pith-pipeline@v0.9.0 · 5634 in / 1052 out tokens · 27496 ms · 2026-05-25T20:00:51.287958+00:00 · methodology

discussion (0)

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Reference graph

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