Resilient fixed-time cooperative output regulation of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs

Wenji Cao; Lu Liu; Dan Zhang; Gang Feng

doi:10.1016/j.automatica.2026.112836

Resilient fixed-time cooperative output regulation of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs

Wenji Cao
, Lu Liu
, Dan Zhang
, Gang Feng^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

2 Citations (Scopus)

Abstract

This paper investigates the resilient fixed-time cooperative output regulation problem of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs. First, a novel distributed resilient fixed-time observer is proposed by accounting for denial-of-service attacks and detail-balanced directed graphs. Then, a novel distributed resilient fixed-time controller based on the proposed observer is developed. It is shown that under the proposed distributed controller, the resilient fixed-time cooperative output regulation problem for heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs is solved. Specifically, it is shown that the regulated output converges to zero in fixed time, where the upper bound of the settling time does not depend on the initial conditions of the concerned multi-agent system and is explicitly given. Finally, a simulation example is given to demonstrate the effectiveness of the proposed controller.

© 2026 Elsevier Ltd.

Original language	English
Article number	112836
Number of pages	14
Journal	Automatica
Volume	185
Online published	15 Jan 2026
DOIs	https://doi.org/10.1016/j.automatica.2026.112836
Publication status	Published - Mar 2026

Bibliographical note

Research Unit(s) information for this publication is provided by the author(s) concerned.

Funding

This work was supported by the Research Grants Council of Hong Kong under Projects CityU-11205024 and CityU-11207323, the National Natural Science Foundation of China under Grants U2541213/62373314/62322315, the Fundament Research for the Provincial Universities of Zhejiang under Grant RF-C2024002, and the Zhejiang Provincial Natural Science Foundation of China under Grant LR22F030003. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Yilin Mo under the direction of Editor Christos G. Cassandras.

Research Keywords

Cooperative output regulation
Distributed fixed-time control
Multi-agent systems
Denial-of-service attacks
Detail-balanced directed graphs

RGC Funding Information

RGC-funded

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10.1016/j.automatica.2026.112836

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@article{4890cb74a1c8494985d4395ca5511d3e,

title = "Resilient fixed-time cooperative output regulation of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs",

abstract = "This paper investigates the resilient fixed-time cooperative output regulation problem of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs. First, a novel distributed resilient fixed-time observer is proposed by accounting for denial-of-service attacks and detail-balanced directed graphs. Then, a novel distributed resilient fixed-time controller based on the proposed observer is developed. It is shown that under the proposed distributed controller, the resilient fixed-time cooperative output regulation problem for heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs is solved. Specifically, it is shown that the regulated output converges to zero in fixed time, where the upper bound of the settling time does not depend on the initial conditions of the concerned multi-agent system and is explicitly given. Finally, a simulation example is given to demonstrate the effectiveness of the proposed controller. {\textcopyright} 2026 Elsevier Ltd. ",

keywords = "Cooperative output regulation, Distributed fixed-time control, Multi-agent systems, Denial-of-service attacks, Detail-balanced directed graphs",

author = "Wenji Cao and Lu Liu and Dan Zhang and Gang Feng",

note = "Research Unit(s) information for this publication is provided by the author(s) concerned.",

year = "2026",

month = mar,

doi = "10.1016/j.automatica.2026.112836",

language = "English",

volume = "185",

journal = "Automatica",

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TY - JOUR

T1 - Resilient fixed-time cooperative output regulation of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs

AU - Cao, Wenji

AU - Liu, Lu

AU - Zhang, Dan

AU - Feng, Gang

N1 - Research Unit(s) information for this publication is provided by the author(s) concerned.

PY - 2026/3

Y1 - 2026/3

N2 - This paper investigates the resilient fixed-time cooperative output regulation problem of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs. First, a novel distributed resilient fixed-time observer is proposed by accounting for denial-of-service attacks and detail-balanced directed graphs. Then, a novel distributed resilient fixed-time controller based on the proposed observer is developed. It is shown that under the proposed distributed controller, the resilient fixed-time cooperative output regulation problem for heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs is solved. Specifically, it is shown that the regulated output converges to zero in fixed time, where the upper bound of the settling time does not depend on the initial conditions of the concerned multi-agent system and is explicitly given. Finally, a simulation example is given to demonstrate the effectiveness of the proposed controller. © 2026 Elsevier Ltd.

AB - This paper investigates the resilient fixed-time cooperative output regulation problem of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs. First, a novel distributed resilient fixed-time observer is proposed by accounting for denial-of-service attacks and detail-balanced directed graphs. Then, a novel distributed resilient fixed-time controller based on the proposed observer is developed. It is shown that under the proposed distributed controller, the resilient fixed-time cooperative output regulation problem for heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs is solved. Specifically, it is shown that the regulated output converges to zero in fixed time, where the upper bound of the settling time does not depend on the initial conditions of the concerned multi-agent system and is explicitly given. Finally, a simulation example is given to demonstrate the effectiveness of the proposed controller. © 2026 Elsevier Ltd.

KW - Cooperative output regulation

KW - Distributed fixed-time control

KW - Multi-agent systems

KW - Denial-of-service attacks

KW - Detail-balanced directed graphs

UR - https://www.scopus.com/pages/publications/105027329104

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-105027329104&origin=recordpage

U2 - 10.1016/j.automatica.2026.112836

DO - 10.1016/j.automatica.2026.112836

M3 - RGC 21 - Publication in refereed journal

SN - 0005-1098

VL - 185

JO - Automatica

JF - Automatica

M1 - 112836

ER -

Resilient fixed-time cooperative output regulation of heterogeneous linear multi-agent systems under denial-of-service attacks over detail-balanced directed graphs

Abstract

Bibliographical note

Funding

Research Keywords

RGC Funding Information

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GRF: Fixed-time cooperative control of multi-agent systems under denial-of-service attacks and its application

GRF: Distributed Optimal Self-Deployment Control of Multiple Dynamic Systems subject to Various Uncertainties and Communication Constraints

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