Adversarial Attack using Projected Gradient Method to Direct Data-Driven Control

In this paper, we propose a new algorithm for adversarial attacks to direct data-driven control. In direct data-driven control, the controller is directly designed from input-output data of the system to be controlled without system identification. Previous research has shown that direct data-driven control is vulnerable to adversarial attacks which add small perturbations to the data, and has proposed the directed gradient sign method (DGSM) as a method to generate severe attacks. We introduce a new method, referred to as the iterative directed gradient sign method (IDGSM), based on DGSM and the projected gradient method. Several numerical examples with comparison of IDGSM and DGSM demonstrate that IDGSM generates more sophisticated adversarial attacks than DGSM. Furthermore, we identify the role of the regularization terms through stability analysis using the Lyapunov equation. The regularization term are defense mechanisms against disturbances, and their effectiveness against adversarial attacks has been numerically validated. We provide a theoretical explanation for their effectiveness against attacks.