Safety-Critical Control for Discrete-time Stochastic Systems with Flexible Safe Bounds using Affine and Quadratic Control Barrier Functions

This paper presents a safe controller synthesis of discrete-time stochastic systems using Control Barrier Functions (CBFs). The proposed condition allows the design of a safe controller synthesis that ensures system safety while avoiding the conservative bounds of safe probabilities. In particular, this study focuses on the design of CBFs that provide flexibility in the choice of functions to obtain tighter bounds on the safe probabilities. Numerical examples demonstrate the effectiveness of the approach.