Finite-Time Secure Control of High-OrderChain-Structured Multi-Agent Systems under Denial-of-Service Attacks

WANG Jingyao; SONG Jian; GUO Jinghua; ZENG Zeqin

doi:10.12263/DZXB.20251088

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Finite-Time Secure Control of High-OrderChain-Structured Multi-Agent Systems under Denial-of-Service Attacks

The Theory and Application of Swarm Intelligence Technology in the Information\-Rich Era | 更新时间：2026-06-16

- Finite-Time Secure Control of High-OrderChain-Structured Multi-Agent Systems under Denial-of-Service Attacks
- ACTA ELECTRONICA SINICA Vol. 54, Issue 3, Pages: 981-999(2026)
- 作者机构：
  
  厦门大学自动化系，福建厦门 361000
- 作者简介：
- 基金信息：
  
  Xiamen Natural Science Foundation(3502Z202471004);National Natural Science Foundation of China (NSFC)(62473323;52372419)
- DOI：10.12263/DZXB.20251088
  CLC： TP273;TP18
- Received：10 January 2026，
  
  Accepted：19 March 2026，
  
  Published：25 March 2026
- 稿件说明：
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王靖瑶, 宋健, 郭景华, 等. 拒绝服务攻击下高阶链式结构多智能体系统的有限时间安全控制[J]. 电子学报, 2026, 54(03): 981-999.

WANG Jingyao, SONG Jian, GUO Jinghua, et al. Finite-Time Secure Control of High-OrderChain-Structured Multi-Agent Systems under Denial-of-Service Attacks[J]. Acta Electronica Sinica, 2026, 54(03): 981-999.
王靖瑶, 宋健, 郭景华, 等. 拒绝服务攻击下高阶链式结构多智能体系统的有限时间安全控制[J]. 电子学报, 2026, 54(03): 981-999. DOI：10.12263/DZXB.20251088

WANG Jingyao, SONG Jian, GUO Jinghua, et al. Finite-Time Secure Control of High-OrderChain-Structured Multi-Agent Systems under Denial-of-Service Attacks[J]. Acta Electronica Sinica, 2026, 54(03): 981-999. DOI：10.12263/DZXB.20251088

摘要

本文聚焦拒绝服务（Denial of Service，DoS）攻击环境下，高阶链式结构多智能体系统的有限时间安全控制难题，开展系统性建模、算法设计与理论验证研究。先构建领导者-跟随者高阶链式动力学模型，精准刻画点对点DoS攻击场景，明确受攻击智能体无法收发信息的核心约束，还原真实网络攻击下的通信中断特征。针对攻击引发的通信链路失效、状态信息丢失问题，设计分布式有限时间观测器，实现领导者状态与输入信息的快速精准估计，有效补偿通信中断造成的信息缺失，同时量化分析DoS攻击对观测器收敛时间的影响，严格证明只要攻击周期存在上限，观测器即可保持预期收敛性能。基于反步法设计流程，融合有限时间控制理论，提出适配高阶链式系统特性的安全控制协议，借助李雅普诺夫稳定性理论完成系统稳定性证明，确保系统在攻击干扰下仍能实现有限时间稳定。为验证所提方法的有效性，以轮式移动机器人编队为仿真对象，搭建包含1个领导者与5个跟随者的高阶链式多智能体系统，在总时长3 s的DoS攻击场景下开展数值仿真。结果表明，所设计观测器可在攻击间歇期0.1 s内快速恢复对领导者信息的准确估计，状态观测误差约6 s收敛至零，跟踪误差约7 s实现完全收敛，系统抗攻击恢复速度显著提升。通过与现有基于观测器的分布式有限时间控制方法对比，本文方案在收敛速度、抗干扰能力与跟踪精度上均具备明显优势。同时开展噪声鲁棒性与参数敏感性测试，验证系统在测量噪声干扰下仍能稳定运行，控制参数小幅波动对收敛性能影响微弱，具备良好工程适用性。研究成果完善了DoS攻击下高阶链式多智能体系统安全控制理论体系，可为无人机编队、智能机器人集群、智能电网等易受网络攻击的关键装备与系统，提供有限时间安全协同控制的技术支撑，提升复杂网络环境下系统的运行可靠性与抗毁能力。

Abstract

This paper focuses on the finite-time secure control problem of high-order chain-structured multi-agent systems under denial-of-service (DoS) attacks

and conducts systematic modeling

algorithm design and theoretical verification. Firstly

a high-order chain dynamic model of the leader-follower framework is established

which accurately describes the point-to-point DoS attack scenario and defines the core constraint that attacked agents cannot send or receive information

thus restoring the characteristics of communication interruption under real cyber attacks. To address the issues of communication link failure and state information loss caused by attacks

a distributed finite-time observer is designed to achieve fast and accurate estimation of the leader’s state and input information

effectively compensating for the information loss due to communication interruption. Meanwhile

the impact of DoS attacks on the convergence time of the observer is quantitatively analyzed

and it is rigorously proved that the observer can maintain the expected convergence performance as long as the attack period is upper bounded.Based on the backstepping design procedure and finite-time control theory

a secure control protocol adapted to the characteristics of high-order chain systems is proposed

and the system stability is verified via Lyapunov stability theory

ensuring that the system can achieve finite-time stability despite attack disturbances. To validate the effectiveness of the proposed method

numerical simulations are carried out in a scenario with a total DoS attack duration of 3 seconds

using a wheeled mobile robot formation as the simulation object and constructing a high-order chain multi-agent system with one leader and five followers. The results show that the designed observer can quickly restore accurate estimation of the leader’s information within 0.1 seconds during attack intervals

the state observation error converges to zero in about 6 seconds

and the tracking error achieves complete convergence in about 7 seconds

significantly improving the system’s attack-resistant recovery speed.Compared with the existing observer-based distributed finite-time control methods

the proposed scheme exhibits obvious advantages in convergence speed

anti-interference ability and tracking accuracy. Furthermore

noise robustness and parameter sensitivity tests verify that the system can operate stably under measurement noise interference

and small fluctuations in control parameters have little effect on convergence performance

indicating good engineering applicability. The research results improve the theoretical system of secure control for high-order chain multi-agent systems under DoS attacks

and can provide technical support for finite-time secure cooperative control of key equipment and systems vulnerable to cyber attacks

such as unmanned aerial vehicle formations

intelligent robot swarms

and smart grids

enhancing the operational reliability and survivability of systems in complex network environments.

关键词

Keywords

references

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