  This paper investigates poisoning attacks against data-driven control
methods. This work is motivated by recent trends showing that, in supervised
learning, slightly modifying the data in a malicious manner can drastically
deteriorate the prediction ability of the trained model. We extend these
analyses to the case of data-driven control methods. Specifically, we
investigate how a malicious adversary can poison the data so as to minimize the
performance of a controller trained using this data. We show that identifying
the most impactful attack boils down to solving a bi-level non-convex
optimization problem, and provide theoretical insights on the attack. We
present a generic algorithm finding a local optimum of this problem and
illustrate our analysis in the case of a model-reference based approach, the
Virtual Reference Feedback Tuning technique, and on data-driven methods based
on Willems et al. lemma. Numerical experiments reveal that minimal but
well-crafted changes in the dataset are sufficient to deteriorate the
performance of data-driven control methods significantly, and even make the
closed-loop system unstable.
