Stealthy control signal attacks in scalar LQG systems

The problem of false data injection in a scalar LQG system is studied in this work. An attacker compromises the input stream and modifies the control signals transmitted with the objective of increasing the quadratic cost incurred by the controller. The optimal adversarial control signals are characterized for a finite horizon LQG problem under a stealthiness/detectability constraint. The tradeoff between the increase in quadratic cost, and the detectability of data injection, as measured by the K-L divergence between legitimate and falsified data dynamics, is derived analytically. The optimal adversarial control signals are shown to be Gaussian with the sequence of variances derived as a function of system parameters and the desired cost increase.