Resilient Control Lyapunov Function-based Quadratic Program for Quadrotors Under Cyberattacks

Jinfeng Chen; Kai Wang; Mohamadamin Rajabinezhad; Qin Lin; Sameeha Tasneem; Shan Zuo; Yichao Wang

REVIEW 2 major objections 2 minor 20 references

Reviewed by Pith at T0; open to challenge.

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

A resilient compensational term inserted into the Control Lyapunov Function counters unknown cyberattacks on quadrotor control channels.

2026-06-30 00:57 UTC pith:KFZE2LLF

load-bearing objection The paper adds an adaptive resilient term to an existing CLF-QP for quadrotors to handle cyberattacks, but leaves the unbounded-attack feasibility question open. the 2 major comments →

arxiv 2606.28588 v1 pith:KFZE2LLF submitted 2026-06-26 eess.SY cs.SY

Resilient Control Lyapunov Function-based Quadratic Program for Quadrotors Under Cyberattacks

Yichao Wang , Sameeha Tasneem , Mohamadamin Rajabinezhad , Jinfeng Chen , Qin Lin , Kai Wang , Shan Zuo This is my paper

classification eess.SY cs.SY

keywords quadrotorscyberattacksresilient controlcontrol Lyapunov functionquadratic programextended state observerfault-tolerant control

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper develops a control method to keep quadrotors stable when facing unknown and unbounded cyberattacks on their pseudo-control signals, in addition to wind and aerodynamic disturbances. It modifies the standard Control Lyapunov Function by adding an adaptive compensation term that adjusts in real time to offset the attacks. This modified function is placed inside a quadratic program that optimizes the control inputs while preserving stability. The overall architecture also uses an extended state observer to estimate and reject lumped disturbances. High-fidelity simulations show the quadrotor stays on its intended trajectory in attack scenarios where a conventional proportional-derivative controller loses stability.

Core claim

By designing a resilient compensational term with real-time online adaptation inside the conventional Control Lyapunov Function and embedding the result in a quadratic program, the RCLF-QP controller compensates for maliciously injected unknown and unbounded cyberattacks on the pseudo-control channels while an extended state observer handles lumped disturbances, thereby preventing trajectory divergence where baseline PD feedback fails.

What carries the argument

The Resilient Control Lyapunov Function-based Quadratic Program (RCLF-QP), which augments the standard CLF with an adaptive compensation term to restore stability guarantees under attacks.

Load-bearing premise

A resilient compensational term with real-time online adaptation can be inserted into the conventional CLF to compensate for unknown and unbounded cyberattacks.

What would settle it

A high-fidelity simulation run in which the quadrotor trajectory diverges or the closed-loop system becomes unstable under an injected attack on the pseudo-control channels despite the RCLF-QP controller would falsify the central claim.

If this is right

The quadratic-program framework permits new control objectives and constraints to be added without changing the underlying stability guarantees.
The integrated observer and RCLF-QP together mitigate both lumped external disturbances and adversarial cyberattacks.
The architecture extends prior fault-tolerant results for complete loss of two opposing rotors to also cover malicious attacks.
Stability is preserved even when attacks are unbounded, provided the adaptation term can be computed online.

Where Pith is reading between the lines

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

The same compensation idea could be tested on other underactuated aerial or ground vehicles facing sensor or actuator attacks.
Hardware experiments on a physical quadrotor would reveal whether communication delays affect the real-time adaptation performance.
The QP structure naturally supports adding explicit safety constraints such as minimum altitude or obstacle avoidance alongside the attack compensation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

The paper adds an adaptive resilient term to an existing CLF-QP for quadrotors to handle cyberattacks, but leaves the unbounded-attack feasibility question open.

read the letter

The paper extends a prior fault-tolerant CLF-QP controller for quadrotors that lose two opposing rotors. It inserts a resilient compensational term with real-time online adaptation into the CLF to cancel unknown and unbounded cyberattacks on the pseudo-control channels.

The QP structure is the part that works cleanly. It keeps the stability argument from the CLF while allowing extra constraints and objectives to be added without rewriting the core proof. Pairing the mechanism with the extended state observer for lumped disturbances and wind is a natural fit for the combined physical-plus-cyber scenario. The abstract states that high-fidelity simulations keep the vehicle on trajectory where plain PD feedback fails, which matches the stated motivation.

The soft spot is the unbounded attack case. The adaptation term must generate whatever correction is needed, yet the QP is subject to actuator limits. If the required input exceeds those limits, the QP can become infeasible and the negative-definiteness of the CLF derivative is no longer assured. The manuscript reports successful simulations but gives no scaling of attack magnitude, no feasibility monitoring, and no separate argument that the QP remains solvable when attacks grow without bound. That gap directly touches the central claim.

This is for control engineers who work on resilient UAV methods. A reader already using CLF-QP frameworks will see a usable incremental example. It deserves peer review because the construction is a legitimate extension with a practical target, even if the feasibility analysis for unbounded attacks needs to be added or clarified.

Referee Report

2 major / 2 minor

Summary. The paper develops a Resilient Control Lyapunov Function-based Quadratic Program (RCLF-QP) for quadrotors subject to partial actuator failures, lumped disturbances, and malicious unbounded cyberattacks on pseudo-control channels. It augments a conventional CLF with a real-time adaptive resilient compensational term, integrates this with an extended state observer, and formulates the result as a QP that preserves stability guarantees while incorporating input constraints. High-fidelity simulations are reported to show that the RCLF-QP prevents trajectory divergence in attack scenarios where a baseline PD controller fails.

Significance. If the central claims hold, the construction supplies a systematic, extensible QP-based method for inserting online adaptation against unbounded attacks into CLF frameworks for underactuated systems without sacrificing the underlying Lyapunov guarantees. The explicit handling of cyberattacks on pseudo-controls, together with the observer, would be a useful addition to the fault-tolerant and resilient control literature for quadrotors.

major comments (2)

[RCLF-QP formulation and stability section] The abstract and the RCLF-QP construction assert compensation for unknown and unbounded attacks via real-time adaptation, yet the QP formulation (with its input constraints) contains no feasibility analysis or proof that a feasible solution continues to exist once the required compensation exceeds available actuator authority; this directly affects the claim that stability is maintained for unbounded attacks.
[Simulation results and attack model] No explicit bound, scaling study, or monitoring of the adaptation term is provided to verify that the CLF derivative remains negative definite when attack magnitudes grow without bound and the compensator saturates the controls; the reported simulations therefore do not test the unbounded regime asserted in the abstract.

minor comments (2)

[Abstract] The abstract refers to a 'high-fidelity environment' without naming the simulator, the precise attack injection model on the pseudo-control channels, or the magnitude scaling used in the reported trials.
[Controller design] Notation for the resilient compensational term and its adaptation law should be introduced with an explicit equation number to allow direct reference in the stability argument.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments. We address each major comment point by point below, indicating planned revisions where appropriate.

read point-by-point responses

Referee: [RCLF-QP formulation and stability section] The abstract and the RCLF-QP construction assert compensation for unknown and unbounded attacks via real-time adaptation, yet the QP formulation (with its input constraints) contains no feasibility analysis or proof that a feasible solution continues to exist once the required compensation exceeds available actuator authority; this directly affects the claim that stability is maintained for unbounded attacks.

Authors: We agree that the manuscript lacks an explicit feasibility analysis for the QP under attacks whose compensation exceeds actuator limits. The RCLF-QP minimizes deviation from the nominal input while enforcing the CLF decrease condition and input bounds, but feasibility is not assured for arbitrarily large attacks. In the revision we will add a dedicated discussion of QP feasibility, state that the Lyapunov guarantees apply conditional on feasibility, and revise the abstract to refer to 'unknown attacks of large but compensable magnitude' rather than unbounded attacks. revision: yes
Referee: [Simulation results and attack model] No explicit bound, scaling study, or monitoring of the adaptation term is provided to verify that the CLF derivative remains negative definite when attack magnitudes grow without bound and the compensator saturates the controls; the reported simulations therefore do not test the unbounded regime asserted in the abstract.

Authors: The reported high-fidelity simulations demonstrate failure of the baseline PD controller and success of RCLF-QP under chosen attack magnitudes, but do not include a scaling study or explicit monitoring of the adaptation term and CLF derivative near saturation. We will augment the simulation section with additional runs that vary attack magnitude, plot the adaptation term, and confirm negativity of the CLF derivative for the largest feasible attacks tested. revision: yes

standing simulated objections not resolved

A rigorous proof that the QP remains feasible (and thus stability is guaranteed) for truly unbounded attacks that exceed available actuator authority.

Circularity Check

0 steps flagged

No circularity: derivation builds new RCLF-QP adaptation on cited prior fault-tolerance result without reduction to inputs or self-referential definitions.

full rationale

The paper's core construction introduces a new resilient compensational term with online adaptation inside the CLF to handle unbounded cyberattacks on pseudo-control channels, then embeds it in a QP. This step is presented as a design choice rather than a mathematical reduction to fitted parameters or prior equations. The single self-citation to chen2024quadrotor supplies the baseline fault-tolerant controller for rotor loss but is not invoked to justify the new adaptation law or stability claims for cyberattacks; the abstract explicitly distinguishes the additional challenge addressed here. No equations are shown that equate the proposed compensator to its own data fit, no uniqueness theorem is imported from the same authors to force the form, and no known empirical pattern is merely renamed. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond standard Lyapunov stability and observer assumptions common to the domain.

pith-pipeline@v0.9.1-grok · 5834 in / 1161 out tokens · 41143 ms · 2026-06-30T00:57:48.773290+00:00 · methodology

0 comments

read the original abstract

Ensuring the operational safety of quadrotors under partial actuator failures, lumped external disturbances, and malicious cyberattacks is a critical challenge due to the system's underactuated and highly nonlinear nature. Building on the existing result of a fault-tolerant control approach for a quadrotor experiencing a complete loss of two opposing rotors \cite{chen2024quadrotor}, this letter further addresses the additional challenge of malicious cyberattacks, which could be unknown and unbounded. While the baseline control law, rooted in proportional-derivative (PD) feedback and observer-based decoupling, effectively handles mismatched disturbances, it remains vulnerable to maliciously injected cyberattacks on the pseudo-control channels. To address this, a Resilient Control Lyapunov Function-based Quadratic Program (RCLF-QP) is developed, where a resilient compensational term with real-time online adaptation is designed in the conventional CLF to compensate for the maliciously injected unknown and unbounded attacks. Compared with the PD feedback control, the proposed QP-based constrained optimization control framework provides a systematic and extensible framework that allows new control objectives and constraints to be seamlessly integrated without altering the underlying stability guarantees. The overall proposed controller integrates a model-based extended state observer with the proposed RCLF-QP mechanism to mitigate both lumped disturbances caused by aerodynamics and strong wind, and adversarial cyberattacks injected by malicious adversaries. Simulations in a high-fidelity environment demonstrate that the proposed RCLF-QP control architecture prevents trajectory divergence and system instability in scenarios where the baseline controller fails in maintaining the stability of Quadrotors under malicious attacks.

discussion (0)

Reference graph

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Chen, J., Zhang, F., Hu, B., and Lin, Q., 2024, “Quadrotor Fault-Tolerant Control at High Speed: A Model-Based Extended State Observer for Mis- matched Disturbance Rejection Approach,” IEEE Control Systems Letters

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Zhang, R.-M., Yao, X.-Y., Wang, L., Park, J. H., and Ge, M.-F., 2025, “Distributed fault-tolerant formation game for quadrotor UAVs with hybrid attacks,” IEEE Transactions on Aerospace and Electronic Systems

2025

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Sun, S., Wang, X., Chu, Q., and de Visser, C. D., 2021, “Incremental Non- linear Fault-Tolerant Control of a Quadrotor With Complete Loss of Two Opposing Rotors,” IEEE Transactions on Robotics,37(1), pp. 116–130

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Wu, Y., Ling, G., and Shi, Y., 2025, “Robust Trajectory Tracking Fault- Tolerant Control for Quadrotor UAVs Based on Adaptive Sliding Mode and Fault Estimation,” Computation,13(7), p. 162

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Geng, M.-J., Ding, H.-F., Yao, X.-Y., and Lv, M., 2025, “Resilient distributed quadrotor UAVs game: Addressing FDI and physical attacks,” IEEE Trans- actions on Vehicular Technology

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Shan, Y., Xie, X.-P., and Sun, N., 2025, “Co-design of enhanced fuzzy observer-based estimation and gain-scheduling control for active suspension systems under malicious attacks,” IEEE Transactions on Intelligent Trans- portation Systems

2025

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Safety-Critical fixed-time formation control of quadrotor UAVs with disturbance based on robust control barrier func- tions,

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Relaxed hover solutions for mul- ticopters: Application to algorithmic redundancy and novel vehicles,

Mueller, M. W. and D’Andrea, R., 2016, “Relaxed hover solutions for mul- ticopters: Application to algorithmic redundancy and novel vehicles,” The International Journal of Robotics Research,35(8), pp. 873–889

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Chen, J., Gao, Z., Hu, Y., and Shao, S., 2023, “A general model- based extended state observer with built-in zero dynamics,”arXiv preprint arXiv:2208.12314

work page arXiv 2023

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Yang, J., Li, S., and Chen, W. H., 2012, “Nonlinear disturbance observer- based control for multi-input multi-output nonlinear systems subject to mis- matched disturbances,” International Journal of Control,85(8), pp. 1071– 1082

2012

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1995