  We study the problem of designing attacks to safety-critical systems in which
the adversary seeks to maximize the overall system cost within a model
predictive control framework. Although in general this problem is NP-hard, we
characterize a family of problems that can be solved in polynomial time via a
second-order cone programming relaxation. In particular, we show that positive
systems fall under this family. We provide examples demonstrating the design of
optimal attacks on an autonomous vehicle and a microgrid.
