When Persistency is not Exciting in Data-Driven Predictive Control
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 leakage effects are the main driver for data to represent the dynamics of the system. These findings are reflected in our numerical results. Data-enabled predictive controllers built on datasets with insufficient bandwidth, despite fulfilling standard rank conditions, suffer from severe ill-conditioning and fail to achieve reference tracking.