  Data-driven control of discrete-time and continuous-time systems is of
tremendous research interest. In this paper, we explore data-driven optimal
control of continuous-time linear systems using input-output data. Based on a
density result, we rigorously derive error bounds for finite-order polynomial
approximations of elements of the system behavior. To this end, we leverage a
link between latent variables and flat outputs of controllable systems.
Combined with a continuous-time counterpart of the fundamental lemma by Willems
et al., we characterize the suboptimality resulting from polynomial
approximations in data-driven linear-quadratic optimal control problems.
Finally, we draw upon a numerical example to illustrate our results.
