# Recurrent Control Barrier Functions: A Path Towards Nonparametric Safety Verification

arXiv: https://arxiv.org/abs/2510.02127 · HTML: https://mlsanity.com/paper/2510.02127/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2025.

## Built on by (most cited first, 1 of 1)

- [Symplectic Inductive Bias for Data-Driven Target Reachability in Hamiltonian Systems](https://mlsanity.com/paper/2604.17213/) (2026)

## Abstract (arXiv)

Ensuring the safety of complex dynamical systems often relies on Hamilton-Jacobi (HJ) Reachability Analysis or Control Barrier Functions (CBFs). Both methods require computing a function that characterizes a safe set that can be made (control) invariant. However, the computational burden of solving high-dimensional partial differential equations (for HJ Reachability) or large-scale semidefinite programs (for CBFs) makes finding such functions challenging. In this paper, we introduce the notion of Recurrent Control Barrier Functions (RCBFs), a novel class of CBFs that leverages a recurrent property of the trajectories, i.e., coming back to a safe set, for safety verification. Under mild assumptions, we show that the RCBF condition holds for the signed-distance function, turning function design into set identification. Notably, the resulting set need not be invariant to certify safety. We further propose a data-driven nonparametric method to compute safe sets that is massively parallelizable and trades off conservativeness against computational cost.