  As the complexity of control systems increases, safety becomes an
increasingly important property since safety violations can damage the plant
and put the system operator in danger. When the system dynamics are unknown,
safety-critical synthesis becomes more challenging. Additionally, modern
systems are controlled digitally and hence behave as sampled-data systems,
i.e., the system dynamics evolve continuously while the control input is
applied at discrete time steps. In this paper, we study the problem of control
synthesis for safety-critical sampled-data systems with unknown dynamics. We
overcome the challenges introduced by sampled-data implementation and unknown
dynamics by constructing a set of control barrier function (CBF)-based
constraints. By satisfying the constructed CBF constraint at each sampling
time, we guarantee the unknown sampled-data system is safe for all time. We
formulate a non-convex program to solve for the control signal at each sampling
time. We decompose the non-convex program into two convex sub-problems. We
illustrate the proposed approach using a numerical case study.
