A ZeroSum Game Framework for Optimal Sensor Placement in Uncertain Networked Control Systems under CyberAttacks
Abstract
This paper proposes a gametheoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zerosum game with two players, namely a malicious adversary and a detector. Given a protected performance vertex, we consider a detector, with uncertain system knowledge, that selects another vertex on which to place a sensor and monitors its output with the aim of detecting the presence of the adversary. On the other hand, the adversary, also with uncertain system knowledge, chooses a single vertex and conducts a cyberattack on its input. The purpose of the adversary is to drive the attack vertex as to maximally disrupt the protected performance vertex while remaining undetected by the detector. As our first contribution, the game payoff of the abovedefined zerosum game is formulated in terms of the ValueatRisk of the adversary's impact. However, this game payoff corresponds to an intractable optimization problem. To tackle the problem, we adopt the scenario approach to approximately compute the game payoff. Then, the optimal monitor selection is determined by analyzing the equilibrium of the zerosum game. The proposed approach is illustrated via a numerical example of a 10vertex networked control system.
 Publication:

arXiv eprints
 Pub Date:
 October 2022
 DOI:
 10.48550/arXiv.2210.04091
 arXiv:
 arXiv:2210.04091
 Bibcode:
 2022arXiv221004091N
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control
 EPrint:
 8 pages, 3 figues, Accepted to the 61st Conference on Decision and Control, Cancun, December 2022