Cyber-physical systems are vulnerable to false data injection by adversaries who compromise cyber communication links. In this paper, an infinite horizon linear quadratic Gaussian (LQG) system is considered wherein the control inputs transmitted over cyber links are vulnerable to compromise and false data injection by adversaries. The adversarial cyber-attack is driven to minimize the performance of the LQG system, and the controller is equipped with an intrusion detection system that monitors the sequence of internal physical states to detect adversarial input modification. The problem is formulated as a two-player zero-sum game with the false alarm probability as the reward, wherein the attacker aims to achieve a target increase in controller cost while maximizing the false alarm probability, and a detector who wishes to minimize the false alarm probability while remaining consistent. It is shown that in such a game, an $ \epsilon$ -equilibrium exists. The equilibrium attacker strategy is the one that minimizes the Kullback–Leibler distance between legitimate and falsified state dynamics, and the equilibrium detector strategy is the corresponding likelihood-ratio test. Numerical simulations are presented that showcase the equilibrium strategy pair and the intuitive strategies comparisons.

中文翻译：

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LQG系统中的错误数据注入和检测：一种博弈论方法

网络物理系统容易受到攻击者破坏网络通信链接的错误数据注入的攻击。在本文中，考虑了无限水平线性二次高斯（LQG）系统，其中通过网络链接传输的控制输入容易受到攻击者的破坏和虚假数据注入。驱动对抗性网络攻击以最大程度地降低LQG系统的性能，并且控制器配备有入侵检测系统，该系统监视内部物理状态的顺序以检测对抗性输入的修改。该问题被表述为以错误警报概率作为奖励的两人零和游戏，其中攻击者旨在实现控制器成本的目标增长，同时最大化错误警报概率，以及希望在保持一致的同时将误报可能性最小化的检测器。结果表明，在这样的游戏中，$ \ epsilon $ -平衡存在。平衡攻击者策略是使合法状态和伪造状态动力学之间的Kullback-Leibler距离最小的策略，而平衡检测器策略是相应的似然比检验。数值模拟显示平衡策略对和直观的策略比较。