Design of False Data Injection Attacks in a Cyber-Physical System using Gaussian Distribution

An attacker can modify the actuator inputs, sensor observations, and state of the physical system in a cyber-physical system (CPS), causing errors in the system's proper functioning. It is crucial to investigate a CPS in the presence of all possible attack types to make it resilient. For this, all possible attack sequences must be known. This paper focuses on designing false data injection (FDI) attacks on the physical system, actuator input, and sensor measurement in a CPS, individually and in their combined locations. Each attack sequence follows a Gaussian distribution. We study a discrete linear time-invariant (LTI) CPS with a single sensor and actuator. The system also includes a Kalman filter and a Chi-square ( \(χ²\) ) detector. With a \(χ²\) detector and possible known system parameters, we have proposed seven types of FDI attacks at vulnerable locations based on Kullback-Leibler (KL) divergence. The attacker can remain undetected by carefully planning the attack sequences. The attack increases the state estimation error (SER), and degrades the system's proper operation. The effect of attacks on the detection result and the difference between state estimation error with and without attack is simulated through two examples from the LTI system.