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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (4): 832-841    DOI: 10.3785/j.issn.1008-973X.2025.04.019
    
Finite-time control under denial-of-service attack
Jie YE(),Ting SHI*(),Wenjun YAN
School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China
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Abstract  

For a class of discrete networked control systems subject to external disturbances, the finite-time control problem under denial-of-service (DoS) attacks was investigated. Considering that DoS attacks could occur simultaneously in both the sensor-to-controller (S-C) and controller-to-actuator (C-A) channels, a Markov stochastic process was employed to model the dynamic characteristics of DoS attacks. The closed-loop control system was represented as a Markov jump system with four modes. To mitigate the impact of external disturbances on system performance, a ${\ell _2} - {\ell _\infty }$ performance index was introduced to enhance the disturbance robustness of the closed-loop system. Based on the finite-time boundedness theory, appropriate mode-dependent Lyapunov functions were constructed, and the Lyapunov stability theory was applied to derive the design conditions for the control algorithm. A set of linear matrix inequalities (LMIs) was solved to provide sufficient conditions for the finite-time state feedback controller, ensuring that the system remained stable within a finite time while meeting the specified performance requirements. The effectiveness and practicality of the control algorithm were demonstrated through numerical simulations and an angular positioning system. Simulation results indicated that, under different DoS attack patterns, the control algorithm effectively suppressed system fluctuations and ensured finite-time stability.

Key words： networked control systems      finite-time control      denial-of-service attack      Markov stochastic process      Markov jump system     
Received: 25 January 2024      Published: 25 April 2025
CLC:  TP 273  
Fund:  浙江省自然科学基金资助项目（LY21F030007）.
Corresponding Authors: Ting SHI     E-mail: 221060032@hdu.edu.cn;tingshi@hdu.edu.cn
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Jie YE
Ting SHI
Wenjun YAN
Cite this article:

Jie YE,Ting SHI,Wenjun YAN. Finite-time control under denial-of-service attack. Journal of ZheJiang University (Engineering Science), 2025, 59(4): 832-841.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.04.019     OR     https://www.zjujournals.com/eng/Y2025/V59/I4/832


拒绝服务攻击下的有限时间控制

针对遭受外部干扰的离散网络控制系统，研究在拒绝服务(DoS)攻击下的有限时间控制问题. 考虑到DoS攻击可能同时存在于传感器-控制器(S-C)通道和控制器-执行器(C-A)通道，采用马尔可夫随机过程对DoS攻击的动态特性进行建模，将闭环控制系统表示为具有4个模态的马尔可夫跳变系统. 为了降低外部干扰对系统性能的影响，引入${\ell _2} - {\ell _\infty }$性能指标，增强闭环系统的抗干扰鲁棒性. 基于有限时间有界理论，构建适当的模态依赖李雅普诺夫函数，应用李雅普诺夫稳定性理论推导出控制算法的设计条件. 通过求解线性矩阵不等式(LMIs)，给出有限时间状态反馈控制器的充分条件，确保系统在有限时间内保持稳定并满足给定的性能要求. 通过数值仿真和角度定位系统验证该控制算法的有效性及实用性. 仿真结果表明，在不同的DoS攻击模式下，该控制算法能够有效抑制系统的波动并保证系统在有限时间内的稳定性.


关键词： 网络控制系统,  有限时间控制,  拒绝服务攻击,  马尔可夫随机过程,  马尔可夫跳变系统 
Fig.1 Structure of network control system
Fig.2 Variation trend of state response variables, control inputs and bounded variables for single simulation and multiple simulation averages (example one)
Fig.3 Variation of denial-of-service attack mode under different transition matrices
Fig.4 Variation tend of state response variables and bounded variables for multiple simulation averages
Fig.5 Variation trend of state response variables, control inputs and bounded variables for single simulation and multiple simulation average (example two)
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