DoS Attacks on Remote State Estimation: A Game-Theoretic Approach With Incomplete Information

In the paper, we address the security challenges involved in the remote estimation of Cyber-Physical Systems under Denial-of-Service (DoS) attacks. To capture the interactive decision-making process between the attacker and the sensor, we propose a game framework with incomplete information, where the sensor (defender) possesses only statistical knowledge regarding the presence of DoS attacks. Both the attacker and the sensor operate under energy constraints. In our approach, we adopt a novel reward function within a single-subsystem CPS, and leverage matrix game theory to obtain the best-response strategies for both sides, leading to a Nash equilibrium. Furthermore, we extend the analysis to the attack-defense problem in CPSs with multiple subsystems, utilizing game theory as the basis. To address the computational complexity, we formulate the problem as an expected energy constraint problem, which reduces the computational cost compared to the original energy constraint problem. We also establish the existence conditions for Nash equilibrium strategies.