  Uncertainties arising in various control systems, such as robots that are
subject to unknown disturbances or environmental variations, pose significant
challenges for ensuring system safety, such as collision avoidance. At the same
time, safety specifications are getting more and more complex, e.g., by
composing multiple safety objectives through Boolean operators resulting in
non-smooth descriptions of safe sets. Control Barrier Functions (CBFs) have
emerged as a control technique to provably guarantee system safety. In most
settings, they rely on an assumption of having deterministic dynamics and
smooth safe sets. This paper relaxes these two assumptions by extending CBFs to
encompass control systems with stochastic dynamics and safe sets defined by
non-smooth functions. By explicitly considering the stochastic nature of system
dynamics and accommodating complex safety specifications, our method enables
the design of safe control strategies in uncertain and complex systems. We
provide formal guarantees on the safety of the system by leveraging the
theoretical foundations of stochastic CBFs and non-smooth safe sets. Numerical
simulations demonstrate the effectiveness of the approach in various scenarios.
