False Data Injection and Detection in LQG Systems: A Game Theoretic Approach

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 ε-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.