Concurrent Receding Horizon Control and Estimation Against Stealthy Attacks

In this article, we consider a game-theoretic framework for cyber-physical systems, where a defender develops a mitigation strategy against an intelligent attacker who exploits the system's uncertainty to remain undetected. The goal of the defender is to optimize a performance cost constructed specifically to account for robustness against stealthy attacks so that the system is regulated. Conversely, the goal of the attacker is to disrupt the system's performance by leveraging its significant information advantage against the defender. Both players implement their policies in a moving horizon fashion, according to the principles of receding horizon control. However, because the defender has no access to the full state of the system, it concurrently employs receding horizon estimation to overcome this limitation. Rigorous theoretical analysis shows that such a concurrent policy can guarantee closed-loop boundedness, despite the stealthy attacks and the information disadvantage. Simulations verify and clarify these findings.