On the Computation of Worst Attacks: a LP Framework

We consider the problem of false data injection attacks modeled as additive disturbances in various parts of a general LTI feedback system and derive necessary and sufficient conditions for the existence of stealthy unbounded attacks. We also consider the problem of characterizing the worst, bounded and stealthy attacks. This problem involves a maximization of a convex function subject to convex constraints, and hence, in principle, it is not easy to solve. However, by employing a $\ell_\infty$ framework, we show how tractable Linear Programming (LP) methods can be used to obtain the worst attack design. Moreover, we provide a controller synthesis iterative method to minimize the worst impact of such attacks.