Attack-Isolation-Based Resilient Control of Large-Scale Systems Against Collusive Attacks

This paper investigates the resilient stability problem of large-scale systems under covert attacks. Covert attacks are difficult to detect, and the collusion among attacks on different subsystems makes the problem more challenging. To address this issue, a two-stage fixed-time observer is introduced for each subsystem to make the covert attack be exposed to its neighboring subsystems. Based on this, an attack isolation algorithm is developed against non-collusive covert attacks, and the notion of
$r^*$
-isolability is introduced to provide a necessary and sufficient condition for the success of attack isolation under the algorithm. To deal with collusive covert attacks, another attack isolation algorithm is further designed, and the notion of
$(r,s)$
-isolability is used to provide a sufficient condition for the effectiveness of the algorithm. Based on the proposed attack isolation techniques, a control law is developed to ensure the resilient stability of the system. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.