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

TL;DR

This paper introduces a novel safe control synthesis method for discrete-time stochastic systems using flexible Control Barrier Functions, enabling tighter safety bounds and improved system safety without overly conservative constraints.

Contribution

It proposes a new condition for designing flexible CBFs that achieve less conservative safety probability bounds in stochastic systems.

Findings

Numerical examples validate the effectiveness of the proposed approach.

The method achieves tighter safety bounds compared to traditional CBFs.

The approach enhances safety guarantees in stochastic control systems.

Abstract

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.