Safety-Critical Control Design for Stochastic Systems Using Control Barrier Functions

This paper proposes new types of control barrier functions, called almost sure reciprocal control barrier function (AS-RCBF) and almost sure zeroing control barrier function (AS-ZCBF), to ensure the safety of stochastic systems with probability one. It also introduces a stochastic zeroing control barrier function (Stochastic ZCBF) to evaluate the probability of a trajectory staying in a safe set. The paper provides control design strategies based on these barrier functions and demonstrates their effectiveness through examples.