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浙江大学学报(工学版)
浙江大学学报(工学版)  2025, Vol. 59 Issue (4): 832-841    DOI: 10.3785/j.issn.1008-973X.2025.04.019
计算机技术与控制工程     
拒绝服务攻击下的有限时间控制
叶洁(),石厅*(),闫文君
杭州电子科技大学 自动化学院，浙江 杭州 310018
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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摘要：

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    
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
收稿日期: 2024-01-25 出版日期: 2025-04-25
CLC:  TP 273  
基金资助: 浙江省自然科学基金资助项目（LY21F030007）.
通讯作者: 石厅     E-mail: 221060032@hdu.edu.cn;tingshi@hdu.edu.cn
作者简介: 叶洁（1999—），男，硕士生，从事网络控制系统安全研究. orcid.org/0009-0001-1295-3023. E-mail：221060032@hdu.edu.cn
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引用本文:

叶洁,石厅,闫文君. 拒绝服务攻击下的有限时间控制[J]. 浙江大学学报(工学版), 2025, 59(4): 832-841.

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.

链接本文:

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

图 1  网络控制系统结构
图 2  状态响应变量、控制输入和有界变量的单次仿真及多次仿真平均值的变化趋势（示例1）
图 3  不同转移矩阵下拒绝服务攻击模态的变化情况
图 4  状态响应变量和有界变量的多次仿真平均值变化趋势
图 5  状态响应变量、控制输入和有界变量的单次仿真及多次仿真平均值的变化趋势（示例2）
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