针对拒绝服务攻击的网络物理系统的弹性极值搜索控制
Resilient Extremum Seeking Control for Cyber-Physical Systems Under Denial-of-Service Attacks
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- Rio de Janeiro State University（里约热内卢州立大学）
- University of California San Diego（加州大学圣地亚哥分校）
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中文总结 AI 辅助
针对DoS攻击下的网络物理系统，提出一种基于保持最近成功传输信号的弹性离散时间极值搜索控制架构，证明其在确定性及概率性攻击下的收敛性，并揭示零输入策略与抖动同步攻击可导致优化偏差。
中文摘要 AI 辅助
极值搜索控制（ESC）依赖于刻意注入的激励来从测量输出中提取优化信息，这使得其网络化实现特别容易受到拒绝服务（DoS）攻击。本文针对遭受DoS攻击的网络物理系统，提出了一种弹性的离散时间ESC架构。通过在DoS攻击期间保持最近成功传输的信号，所提出的机制在成功通信下产生具有指数收缩模式的平均误差动态，在攻击下产生中性模式。对于确定性DoS攻击，在攻击持续时间的平均界限下，建立了对极值的实际指数收敛性，其显式收敛速率取决于受攻击时间比例。对于概率性DoS攻击，通过随机平均建立了几乎必然收敛和依概率收敛性质，攻击成功概率显式地进入收敛速率。一个关键发现是，看似自然的零输入策略可能从根本上损害ESC：与抖动同步的攻击在平均动态中产生$\mathcal{O}(1/a)$的偏差，其中$a$是抖动幅度，并可能将平衡点从真实最优解处移开。因此，在所提出的基于保持的架构下，只要通信未被永久阻断，日益严重的DoS攻击主要会减慢优化过程，而不会破坏其稳定性。数值模拟验证了理论保证以及由抖动同步攻击引发的失效机制。
英文摘要
Extremum seeking control (ESC) relies on deliberately injected excitation to extract optimization information from measured outputs, making its networked implementation particularly vulnerable to denial-of-service (DoS) attacks. This paper develops a resilient discrete-time ESC architecture for cyber-physical systems subject to DoS attacks. By holding the most recently successfully transmitted signals during DoS intervals, the proposed mechanism yields averaged error dynamics with an exponentially contracting mode under successful communication and a neutral mode under attack. For deterministic DoS attacks, practical exponential convergence to the extremum is established under an average bound on the attack duration, with an explicit convergence rate depending on the fraction of time under attack. For probabilistic DoS attacks, almost-sure and in-probability convergence properties are established via stochastic averaging, with the attack success probability explicitly entering the convergence rate. A key finding is that a seemingly natural zero-input strategy can fundamentally compromise ESC: attacks synchronized with the dither generate an $\mathcal{O}(1/a)$ bias in the averaged dynamics, where $a$ is the dither amplitude, and can displace the equilibrium from the true optimizer. Thus, under the proposed hold-based architecture, increasingly severe DoS attacks primarily slow the optimization process rather than destroy its stability, provided that communication is not permanently blocked. Numerical simulations illustrate the theoretical guarantees and the failure mechanism induced by dither-synchronized attacks.
