Strategic sensor placement on graphs

Abstract

Abstract This paper studies optimal sensor placement in networked control systems for improving the detectability of cyber–physical attacks. The problem is formulated as a game between an attacker and a detector. The attacker’s decision is to select a set of nodes in the network to attack, and the detector’s decision is to places sensors on a set of nodes. The detector tries to maximize the detectability of attack signals. The attacker tries to maximize its impact while avoiding detection. We analyze the game using structured systems theory and other graph-theoretic concepts. The equilibrium strategy of the detector determines the optimal locations of the sensors. We study pure and mixed strategies for the case of single attacked–single detected nodes. We extend some of our results to the case of multiple attacked–multiple detected nodes. For the cases where the game does not admit a Nash equilibrium, we discuss the Stackelberg game and give graph-theoretic bounds on the game value. Finally, we discuss the Stackelberg equilibrium strategies for simple graph topologies.