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arXiv · 2507.17703

Piecewise Control Barrier Functions for Stochastic Systems

Rayan Mazouz·Luca Laurenti·Morteza Lahijanian
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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.

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Rayan Mazouz, Luca Laurenti, Morteza Lahijanian. 2025-07-23. Piecewise Control Barrier Functions for Stochastic Systems. https://arxiv.org/abs/2507.17703

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