A Graph Theoretic Characterization of Perfect Attackability and Detection in Distributed Control Systems

TL;DR

This paper characterizes the detectability of integrity attacks in distributed control systems using graph theory, providing conditions and network design principles to prevent undetectable malicious actions.

Contribution

It introduces a graph-theoretic framework for analyzing and designing secure DCSs, linking structural left invertibility to vertex separators for attack detection.

Findings

Graph-theoretic conditions for attack detectability

Design of minimal communication networks for security

Numerical validation of theoretical results

Abstract

This paper is concerned with the analysis and design of secure Distributed Control Systems in the face of integrity attacks on sensors and controllers by external attackers or insiders. In general a DCS consists of many heterogenous components and agents including sensors, actuators, controllers. Due to its distributed nature, some agents may start misbehaving to disrupt the system. This paper first reviews necessary and sufficient conditions for deterministic detection of integrity attacks carried out by any number of malicious agents, based on the concept of left invertibility of structural control systems. It then develops a notion equivalent to structural left invertibility in terms of vertex separators of a graph. This tool is then leveraged to design minimal communication networks for DCSs, which ensure that an adversary cannot generate undetectable attacks. Numerical examples are included to illustrate these results.