Physics-informed data-driven control without persistence of excitation

We show that data that is not sufficiently informative to allow for system re-identification can still provide meaningful information when combined with external or physical knowledge of the system, such as bounded system matrix norms. We then illustrate how this information can be leveraged for safety and energy minimization problems and to enhance predictions in unmodelled dynamics. This preliminary work outlines key ideas toward using limited data for effective control by integrating physical knowledge of the system and exploiting interpolation conditions.