The problem of learning-to-control relaxation systems from data is considered. It is shown that the equi-librium of the relaxation system's step response defines the solution of a class of robust control problems and provides a good suboptimal solution to a class of linear quadratic regulator problems. These results demonstrate the potential to efficiently learn policies for these control problems from a single, easy-to-implement trajectory data point, being the step response. More broadly, these results highlight how the system structure and problem definition of the control problem can be exploited to generate data efficient learning- to-control methods.