  Modern nonlinear control theory seeks to endow systems with properties such
as stability and safety, and has been deployed successfully across various
domains. Despite this success, model uncertainty remains a significant
challenge in ensuring that model-based controllers transfer to real world
systems. This paper develops a data-driven approach to robust control synthesis
in the presence of model uncertainty using Control Certificate Functions
(CCFs), resulting in a convex optimization based controller for achieving
properties like stability and safety. An important benefit of our framework is
nuanced data-dependent guarantees, which in principle can yield
sample-efficient data collection approaches that need not fully determine the
input-to-state relationship. This work serves as a starting point for
addressing important questions at the intersection of nonlinear control theory
and non-parametric learning, both theoretical and in application. We validate
the proposed method in simulation with an inverted pendulum in multiple
experimental configurations.
