Designing Optimal Stealthy False Data Injection Attacks in Cyber-Physical Systems: Leveraging Historical Data and Kullback–Leibler Divergence Constraints

In the rapidly evolving landscape of Cyber-Physical Systems (CPS), understanding potential vulnerabilities through the design of sophisticated attack strategies is crucial for developing robust defense mechanisms. This paper focuses on formulating innovative False Data Injection (FDI) attack strategies that leverage current and historical data under relaxed stealthiness constraints, measured by the Kullback-Leibler Divergence (KLD). By exploring the trade-offs between attack performance and detection risk, we propose two types of attack policies that not only enhance the effectiveness of the attacks but also offer practical implementation benefits. The optimal attack parameters are derived analytically, enabling efficient offline pre-calculation and real-time deployment. Finally, simulation studies on a satellite system validate the superiority of our strategies over existing methods, demonstrating the ability to maximize disruption while maintaining stealthiness. This research not only deepens our understanding of CPS vulnerabilities but also lays the groundwork for more resilient defense strategies by anticipating and countering sophisticated attacks.