
This study explores the vulnerability of direct data driven control, particularly in the linear quadratic regulator (LQR) problem, to adversarial perturbations in offline collected data. We focus on stealthy attacks that subtly alter training data to destabilize the closed-loop system while evading detection. To craft such attacks, we propose Directed Gradient Sign Method (DGSM) and its iterative variant (I-DGSM), which adapt techniques from adversarial machine learning to align perturbations with the gradient of the closed-loop spectral radius. A key technical contribution is an efficient and exact gradient computation method using implicit differentiation through the Karush-Kuhn-Tucker conditions of the underlying semidefinite program. For defense, we introduce two strategies: (i) regularization to reduce controller sensitivity, and (ii) robust data-driven control that ensures stability under bounded perturbations. Experiments across benchmark systems reveal that even imperceptibly small perturbations, up to ten times smaller than random noise, can lead to instability, while the proposed defenses significantly reduce attack success rates with minimal performance loss. We also assess transferability under partial knowledge, demonstrating the importance of protecting training data. This work highlights critical security risks in data driven control and proposes practical methods for both attack and defense.
17 pages, Accepted Manuscript in Automatica
FOS: Electrical engineering, electronic engineering, information engineering, Systems and Control (eess.SY), Systems and Control
FOS: Electrical engineering, electronic engineering, information engineering, Systems and Control (eess.SY), Systems and Control
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 0 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
