  High performance tracking control can only be achieved if a good model of the
dynamics is available. However, such a model is often difficult to obtain from
first order physics only. In this paper, we develop a data-driven control law
that ensures closed loop stability of Lagrangian systems. For this purpose, we
use Gaussian Process regression for the feed-forward compensation of the
unknown dynamics of the system. The gains of the feedback part are adapted
based on the uncertainty of the learned model. Thus, the feedback gains are
kept low as long as the learned model describes the true system sufficiently
precisely. We show how to select a suitable gain adaption law that incorporates
the uncertainty of the model to guarantee a globally bounded tracking error. A
simulation with a robot manipulator demonstrates the efficacy of the proposed
control law.
