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

TL;DR

This paper introduces a game-theoretic framework for optimal sensor placement in networked control systems to detect cyber-attacks, using zero-sum game analysis and Nash equilibrium computation.

Contribution

It formulates the sensor placement problem as a zero-sum game and provides algebraic conditions for feasible monitoring strategies, advancing the design of attack detection mechanisms.

Findings

Characterized the game payoff for specific attack and monitor vertices.

Derived algebraic conditions for feasible monitor vertices.

Demonstrated the approach with a numerical example on a 10-vertex network.

Abstract

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