基于双域多项式框架的随机非线性CPS安全增益调度方法

doi:10.3969/j.issn.1671-1122.2025.12.005

摘要/Abstract

摘要：

在非线性信息物理系统（CPS）中，随机突变与非线性特性通常同时存在，并受到复杂转移概率与网络攻击的干扰，这为系统的安全与稳定控制带来了严峻挑战。文章提出一种基于双域多项式框架的随机非线性CPS安全增益调度方法，该方法结合模糊建模与马尔可夫跳变系统建立模型，更精确地刻画非线性动态与随机突变行为。在结构域中引入多胞体重构策略，将不精确和部分未知的转移概率转化为多胞体形式，以克服传统方法在复杂概率环境下的局限性。在控制设计域中，利用齐次多项式Lyapunov函数和控制器结构，有效降低设计保守性并提升鲁棒性。理论分析结果表明，该方法在拒绝服务攻击下仍可保证指数均方稳定性与预设性能指标。仿真结果进一步验证了文章所提方法的有效性，显示其在可行解域扩展和性能指标优化方面均优于现有方法，能够为复杂概率与网络威胁环境下的工业CPS安全控制提供一种可行的解决方案。

关键词: CPS, 马尔可夫跳变系统, 模糊系统, DoS攻击

Abstract:

In nonlinear cyber-physical systems(CPS), random switching behaviors and nonlinear characteristics often coexist, while complex transition probabilities and cyber attacks further threaten system safety and stability. This paper proposed a secure gain-scheduling method for stochastic nonlinear CPS based on dual-domain polynomial framework. This method was constructed by integrating fuzzy modeling with Markov jump systems, which enabled accurate characterization of nonlinear dynamics and stochastic switching phenomena. A polytopic reconstruction strategy in the structural domain was introduced to transform imprecise and partially unknown transition probabilities into a tractable form, thereby avoiding infeasibility under complex probabilistic environments. In the control design domain, homogeneous polynomial Lyapunov functions and controller structures were employed to effectively reduce conservatism and enhance robustness. Theoretical analysis results indicate that the proposed method guarantees exponential mean-square stability and performance optimization even under denial-of-service attacks and other cyber threats. Numerical simulations further verify the effectiveness of the proposed approach, showing its superiority in expanding the feasible solution domain and improving performance indices. The results provide a practical solution for secure control of CPS operating under complex probabilistic and adversarial conditions.

Key words: CPS, Markov jump system, fuzzy system, DoS attack

中图分类号:

TP309

解相朋, 邵邢晨. 基于双域多项式框架的随机非线性CPS安全增益调度方法[J]. 信息网络安全, 2025, 25(12): 1889-1900.

XIE Xiangpeng, SHAO Xingchen. Secure Gain-Scheduling Method for Stochastic Nonlinear CPS Based on Dual-Domain Polynomial Framework[J]. Netinfo Security, 2025, 25(12): 1889-1900.

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参数	模式一	模式二
$m_s$/kg	2.45	2.90
$m_u$/kg	1	1
$c_s$/（Ns·m^-1）	7.5	7.5
$k_s(t)$/（N·m^-1）	[750,900]	[750,900]
$k_u$/（N·m^-1）	2500	2500
$c_u$/（Ns·m^-1）	5	5