When Persistency is not Exciting in Data-Driven Predictive Control

Abstract

Understanding how to collect data that is meaningful for control purposes is of paramount importance in data-driven control. While existing approaches have primarily relied on the satisfaction of a rank condition to assess the quality of an experiment, we show that satisfying it is not always sufficient to achieve satisfactory closed-loop performance. Focusing on scenarios where white-noise-like excitation cannot be used for data collection, we examine the frequency-domain implications of linear behavioral representation. This analysis demonstrates that data must both satisfy the rank condition and excite the frequencies of interest for the control goal, thereby laying the foundations for control-oriented experiment design tailored to direct data-driven approaches. These findings are reflected in our numerical results. Data-enabled predictive controllers that rely on data satisfying the rank condition but neglect the tracking control goal result in a closed-loop system that cannot track the selected reference.