  The combination of machine learning with control offers many opportunities,
in particular for robust control. However, due to strong safety and reliability
requirements in many real-world applications, providing rigorous statistical
and control-theoretic guarantees is of utmost importance, yet difficult to
achieve for learning-based control schemes. We present a general framework for
learning-enhanced robust control that allows for systematic integration of
prior engineering knowledge, is fully compatible with modern robust control and
still comes with rigorous and practically meaningful guarantees. Building on
the established Linear Fractional Representation and Integral Quadratic
Constraints framework, we integrate Gaussian Process Regression as a learning
component and state-of-the-art robust controller synthesis. In a concrete
robust control example, our approach is demonstrated to yield improved
performance with more data, while guarantees are maintained throughout.
