  Despite the existence of formal guarantees for learning-based control
approaches, the relationship between data and control performance is still
poorly understood. In this paper, we propose a Lyapunov-based measure for
quantifying the impact of data on the certifiable control performance. By
modeling unknown system dynamics through Gaussian processes, we can determine
the interrelation between model uncertainty and satisfaction of stability
conditions. This allows us to directly asses the impact of data on the provable
stationary control performance, and thereby the value of the data for the
closed-loop system performance. Our approach is applicable to a wide variety of
unknown nonlinear systems that are to be controlled by a generic learning-based
control law, and the results obtained in numerical simulations indicate the
efficacy of the proposed measure.
