Piecewise Control Barrier Functions for Stochastic Systems
Abstract
This paper presents a method for the simultaneous synthesis of a barrier certificate and a safe controller for discrete-time nonlinear stochastic systems. Our approach, based on piecewise stochastic control barrier functions, reduces the synthesis problem to a minimax optimization, which we solve exactly using a dual linear program with zero gap. This enables the joint optimization of the barrier certificate and safe controller within a single formulation. The method accommodates stochastic dynamics with additive noise and a bounded continuous control set. The synthesized controllers and barrier certificates provide a formally guaranteed lower bound on probabilistic safety. Case studies on linear and nonlinear stochastic systems validate the effectiveness of our approach.
Cite
@article{arxiv.2507.17703,
title = {Piecewise Control Barrier Functions for Stochastic Systems},
author = {Rayan Mazouz and Luca Laurenti and Morteza Lahijanian},
journal= {arXiv preprint arXiv:2507.17703},
year = {2025}
}