15 janvier 2026
Titre : Willems’ Lemma Reformulations for DeePC: Which Operators Preserve LTI System Behavior?
Résumé : This work investigates the computational efficiency of Data-EnablEd Predictive Control (DeePC) reformulations. Based on Willems’ fundamental lemma, this control method uses Hankel matrices to represent system dynamics. Various reformulations of the lemma have been proposed in the literature, for instance, using frequency-domain data. In this work, we show that all reformulations are necessarily based on linear shift-invariant transformations, which have the fundamental property that they preserve the trajectory space of all LTI systems. Our results unify the existing reformulations and provide guidelines for designing novel ones.