Real-time Attack-recovery for Cyber-physical Systems Using Linear-quadratic Regulator

The increasing autonomy and connectivity in cyber-physical systems (CPS) come with new security vulnerabilities that are easily exploitable by malicious attackers to spoof a system to perform dangerous actions. While the vast majority of existing works focus on attack prevention and detection, the key question is "what to do after detecting an attack?". This problem attracts fairly rare attention though its significance is emphasized by the need to mitigate or even eliminate attack impacts on a system. In this article, we study this attack response problem and propose novel real-time recovery for securing CPS. First, this work's core component is a recovery control calculator using a Linear-Quadratic Regulator (LQR) with timing and safety constraints. This component can smoothly steer back a physical system under control to a target state set before a safe deadline and maintain the system state in the set once it is driven to it. We further propose an Alternating Direction Method of Multipliers (ADMM) based algorithm that can fast solve the LQR-based recovery problem. Second, supporting components for the attack recovery computation include a checkpointer, a state reconstructor, and a deadline estimator. To realize these components respectively, we propose (i) a sliding-window-based checkpointing protocol that governs sufficient trustworthy data, (ii) a state reconstruction approach that uses the checkpointed data to estimate the current system state, and (iii) a reachability-based approach to conservatively estimate a safe deadline. Finally, we implement our approach and demonstrate its effectiveness in dealing with totally 15 experimental scenarios which are designed based on 5 CPS simulators and 3 types of sensor attacks.