# Converse Barrier Certificates for Finite-time Safety Verification of Continuous-time Perturbed Deterministic Systems

arXiv: https://arxiv.org/abs/2402.17167 · HTML: https://mlsanity.com/paper/2402.17167/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2024.

## Built on by (most cited first, 2 of 2)

- [Unifying Hamilton-Jacobi Reachability and Reinforcement Learning](https://mlsanity.com/paper/2601.08050/) (2026)
- [Reachability-Preserving Bellman Operator for the Discounted Reach-Cost Value Function: Uniting Hamilton-Jacobi Reachability and Reinforcement Learning](https://mlsanity.com/paper/2607.07893/) (2026)

## Abstract (arXiv)

In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time horizon, if the system is safe, it, starting from a compact initial set, will remain within an open and bounded safe region throughout the specified time horizon, regardless of the disturbances. The main contribution of this work is a converse theorem: we prove that a continuously differentiable, time-dependent barrier certificate exists if and only if the system is safe over the finite-time horizon. The existence problem is explored by finding a continuously differentiable approximation of a unique Lipschitz viscosity solution to a Hamilton-Jacobi equation.