Data-Driven Control from Poisoned Data: Fundamental Limitations and Secure DeePC

Abstract: We study a data-driven control problem in the presence of arbitrary data poisoning attacks. We assume that a subset of offline output data is stored in unprotected locations and may be poisoned by an adversary. We first establish fundamental limitations for data-driven control arising from such poisoned data: poisoning attacks are not detected/identified from the dataset alone; unprotected data are non-informative for controller design with worst-case guarantees; and hard constraints on unprotected outputs are not certifiable. Motivated by these limitations and the data-enabled predictive control (DeePC) technique, we propose Secure DeePC, a data-driven control algorithm that is resilient against poisoning attacks. It first runs output-truncated DeePC using only the protected dataset until the online input becomes persistently exciting. It then uses online measurements to reconstruct the partial offline dataset, and finally returns to full-output DeePC. Secure DeePC achieves MPC-equivalent performance in finite time almost surely under certain conditions. Simulation results illustrate the efficacy of the proposed framework against poisoning attacks.