A Single-Adversary-Single-Detector Zero-Sum Game in Networked Control Systems*

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement for detecting cyber-attacks in networked control systems. The is formulated as zero-sum game with two players, namely malicious adversary and detector. Given protected target vertex, detector places at single vertex monitor system detect presence adversary. On other hand, selects through which conduct cyber-attack that maximally disrupts while remaining undetected by As our first contribution, given pair attack vertices known payoff function defined output-to-output gain respective system. Then, characterizes set feasible actions ensures bounded values payoff. Finally, an algebraic sufficient condition proposed examine whether belongs vertices. then determined computing mixed-strategy Nash equilibrium linear programming. illustrated via numerical example 10-vertex vertex.