Linear Quadratic Gaussian Control under False Data Injection Attacks

In a false data injection attack, an adversary compromises one or more sensors of a networked system and introduces false measurements in order to bias the control and degrade the system performance. In this paper, we investigate the problem of designing controllers for linear systems with Gaussian noise in order to minimize a quadratic cost under both normal operating conditions and false data injection attacks. We develop a two-stage approach, in which the controller chooses a set of admissible control signals in the first stage, which limits the worst-case damage that the adversary can cause by introducing false data. The control action at each time step is then selected at the second stage. We demonstrate that both stages can be solved optimally using convex optimization techniques and present efficient algorithms for choosing the optimal control policy. Our approach is evaluated through numerical study.