SCO Seminar - Amir Shakouri & Yongzhang Li, University of Groningen

Title: On the fragility of data-driven feedback gains

Abstract:

In this presentation, we study the effect of additive, multiplicative, and directional perturbations on control parameters in a data-based setting. A stabilizing data-driven feedback gain is called fragile if a small error in the gain, no matter how small, could potentially destabilize the true system. It turns out that a rank condition on the input-state data is necessary and sufficient for a data-driven feedback gain to be nonfragile. We also study the case where the closed-loop system is immune to feedback perturbations, for which necessary and sufficient conditions are provided. For each class of perturbations, we present a ball with respect to the spectral norm such that the stability of the unknown true system is guaranteed under feedback perturbations within such a ball. The presented solutions are either expressed in closed form, or obtainable by solving a semi-definite program.