Necessary and Sufficient Conditions for Data-driven Model Reference Control

The objective of model reference control is to design a controller that regulates the system's behavior so as to match a specified reference model. This paper investigates necessary and sufficient conditions for model reference control from a data-driven perspective, when only a set of data generated by the system is utilized to directly accomplish the matching. Noiseless and noisy data settings are both considered. Notably, all methods we propose build on the concept of data informativity and do not rely on persistently exciting data.