  This paper presents a tractable framework for data-driven synthesis of
robustly safe control laws. Given noisy experimental data and some priors about
the structure of the system, the goal is to synthesize a state feedback law
such that the trajectories of the closed loop system are guaranteed to avoid an
unsafe set even in the presence of unknown but bounded disturbances (process
noise). The main result of the paper shows that for polynomial dynamics, this
problem can be reduced to a tractable convex optimization by combining elements
from polynomial optimization and the theorem of alternatives. This optimization
provides both a rational control law and a density function safety certificate.
These results are illustrated with numerical examples.
