A Graph-Theoretic Characterization of Perfect Attackability for Secure Design of Distributed Control Systems

This paper considers secure design in distributed control systems to ensure the detection of stealthy integrity attacks. Distributed control systems consist of many heterogeneous components, such as sensors, controllers, and actuators and may contain several independent agents. The presence of many components and agents in a system increases the attack surfaces for potential adversaries, making distributed control systems vulnerable to malicious behavior. The goal of this paper is to consider the design of distributed control systems to ensure the deterministic detection of attacks. To do this, we leverage existing results which relate the deterministic detection of a fixed set of malicious nodes to structural left invertibility. We extend the notion of structural left invertibility to consider attacks from all possible sets of malicious nodes using vertex separators. Vertex separators are then used to solve optimization problems which aim to minimize communication networks while also ensuring that a resource limited adversary cannot generate perfect attacks. Optimal bounds on communication and sensing are obtained and polynomial time design algorithms are provided.