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

Abstract

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r^*$</tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(r,s)$</tex-math></inline-formula> -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.