Research on the mechanism of industrial control system security risk propagation

WANG Hongmin; WEI Qiang; WANG Lanmin

doi:10.11959/j.issn.2096-109x.2025045

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Research on the mechanism of industrial control system security risk propagation

Topic: Cybersecurity for New Industrialization | 更新时间：2025-09-12

- Research on the mechanism of industrial control system security risk propagation
- Chinese Journal of Network and Information Security Vol. 11, Issue 4, Pages: 107-116(2025)
- 作者机构：
  
  1.信息工程大学，河南郑州 450001
  2.天津工业大学，天津 300000
- 作者简介：
- 基金信息：
- DOI：10.11959/j.issn.2096-109x.2025045
  CLC： TP393
- Received：14 January 2025，
  
  Revised：2025-05-06，
  
  Published：25 August 2025
- 稿件说明：
移动端阅览
王红敏, 魏强, 王兰敏. 工业控制系统安全风险传播机理研究[J]. 网络与信息安全学报, 2025, 11(4): 107-116.

Format: WANG H M, WEI Q, WANG L M. Research on the mechanism of industrial control system security risk propagation[J]. Chinese Journal of Network and Information Security, 2025, 11(4): 107-116.
王红敏, 魏强, 王兰敏. 工业控制系统安全风险传播机理研究[J]. 网络与信息安全学报, 2025, 11(4): 107-116. DOI： 10.11959/j.issn.2096-109x.2025045.

Format: WANG H M, WEI Q, WANG L M. Research on the mechanism of industrial control system security risk propagation[J]. Chinese Journal of Network and Information Security, 2025, 11(4): 107-116. DOI： 10.11959/j.issn.2096-109x.2025045.

摘要

随着工业化和信息化的深度融合，工业控制系统在提升生产效率的同时也面临着日益复杂的安全威胁。深入研究工业控制系统安全风险的传播机理，对保障其安全稳定运行具有重要意义。为此，借鉴生物学中的SIRS（susceptible-infected-recovered-susceptible）模型，研究工业控制系统安全风险传播机理。首先，基于SIRS模型绘制了系统状态转移图，并建立对应的微分方程组。基于该模型，以感染节点的变化率为核心指标分析风险传播速度，识别并量化影响传播速度的关键因素。其次，基于基本再生数

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的阈值特性研究风险传播范围。当

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时，通过构造Lyapunov函数证明系统在无毒平衡点

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处具有全局稳定性，表明风险将随时间逐渐衰减并最终在系统中完全消失；当

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时，通过求解雅可比矩阵的特征方程，证明系统在有毒平衡点

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2.53999996

处具有局部渐进稳定性，揭示风险会在系统内持续稳定传播且不会自行消失的规律。最后，应用最优控制理论研究风险传播的控制问题，利用最优控制定理证明最优控制解的存在性，并通过引入Hamilton函数求解最优控制策略。为验证理论模型的合理性，通过数值模拟与实验分析，分别验证无毒平衡点的全局稳定性与有毒平衡点的局部渐进稳定性，为工业控制系统安全风险的量化评估与精准管控提供理论支撑。

Abstract

With the deep integration of industrialisation and informatisation

industrial control systems (ICS) were faced with increasingly complex security threats while productivity was being enhanced. An in-depth study of the propagation mechanism of industrial control system security risks was conducted to guarantee safe and stable operation. For this purpose

the susceptible–infected–recovered–susceptible (SIRS) infectious disease model from biology was drawn upon to analyse the mechanism of security risk propagation in industrial control systems. The system state transition diagram was constructed based on the SIRS model

and the corresponding system of differential equations was established. Based on this model

the rate of change of infected nodes was used as a core indicator to analyze the speed of risk propagation

and key factors influencing the propagation speed were identified and quantified. The range of risk propagation was studied based on the threshold properties of the basic reproduction number R₀. When R₀ < 1

it was proven that the system exhibited global stability at the disease-free equilibrium point E₀ by constructing a Lyapunov function

indicating that the risk would gradually decay over time and eventually disappear entirely from the system. When R₀ > 1

by solving the characteristic equation of the Jacobian matrix

it was shown that the system achieved local asymptotic stability at the endemic equilibrium point E*

revealing that the risk would propagate steadily within the system and would not disappear autonomously. Optimal control theory was applied to study the control of risk propagation. The existence of an optimal control solution was proven using optimal control theory

and the optimal control strategy was derived by introducing the Hamilton function. To verify the rationality of the theoretical model

the global stability of the disease-free equilibrium point and the local asymptotic stability of the endemic equilibrium point were validated through numerical simulation and experimental analysis

respectively. This study thus provides theoretical support for the quantitative assessment and precise control of safety risks in industrial control systems.

关键词

Keywords

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