A Spectral Perspective on Stochastic Control Barrier Functions
The paper introduces a spectral method to find a natural and valid Stochastic Control Barrier Function (SCBF) for systems with stochastic disturbances. It uses a Koopman-like operator to analyze how safety probability evolves over time. The dominant eigenfunction of this operator quantifies the long-term safety of initial states, while its corresponding eigenvalue measures the global decay rate of safety.