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.

本文研究了在网络控制系统中的最佳传感器位置，以提高网络物理攻击的可检测性。该问题被表述为攻击者和检测者之间的游戏。攻击者的决定是选择网络中的一组节点进行攻击，而检测器的决定是将传感器放置在一组节点上。检测器试图使攻击信号的可检测性最大化。攻击者试图最大程度地发挥影响，同时避免被发现。我们使用结构化系统理论和其他图论概念来分析游戏。检测器的平衡策略确定传感器的最佳位置。我们研究了针对单个被攻击节点（单个检测到的节点）的纯策略和混合策略。我们将一些结果扩展到多个被攻击的节点的情况。对于游戏不允许纳什均衡的情况，我们讨论了Stackelberg游戏，并给出了游戏价值的图论界。最后，我们讨论用于简单图拓扑的Stackelberg平衡策略。