Optimal Detector Placement in Networked Control Systems under Cyber-attacks with Applications to Power Networks

This paper proposes a game-theoretic method to address the problem of optimal detector placement in a networked control system under cyber-attacks. The networked control system is composed of interconnected agents where each agent is regulated by its local controller over unprotected communication, which leaves the system vulnerable to malicious cyber-attacks. To guarantee a given local performance, the defender optimally selects a single agent on which to place a detector at its local controller with the purpose of detecting cyber-attacks. On the other hand, an adversary optimally chooses a single agent on which to conduct a cyber-attack on its input with the aim of maximally worsening the local performance while remaining stealthy to the defender. First, we present a necessary and sufficient condition to ensure that the maximal attack impact on the local performance is bounded, which restricts the possible actions of the defender to a subset of available agents. Then, by considering the maximal attack impact on the local performance as a game payoff, we cast the problem of finding optimal actions of the defender and the adversary as a zero-sum game. Finally, with the possible action sets of the defender and the adversary, an algorithm is devoted to determining the Nash equilibria of the zero-sum game that yield the optimal detector placement. The proposed method is illustrated on an IEEE benchmark for power systems. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)