Learning Secure Control Design for Cyber-Physical Systems Under False Data Injection Attacks

In this study, we employ two data-driven approaches to address the secure control problem for cyber-physical systems when facing false data injection attacks. Firstly, guided by zero-sum game theory and the principle of optimality, we derive the optimal control gain, which hinges on the solution of a corresponding algebraic Riccati equation. Secondly, we present sufficient conditions to guarantee the existence of a solution to the algebraic Riccati equation, which constitutes the first major contributions of this paper. Subsequently, we introduce two data-driven Q-learning algorithms, facilitating model-free control design. The second algorithm represents the second major contribution of this paper, as it not only operates without the need for a system model but also eliminates the requirement for state vectors, making it quite practical. Lastly, the efficacy of the proposed control schemes is confirmed through a case study involving an F-16 aircraft.