# Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference

arXiv: https://arxiv.org/abs/2504.01807 · HTML: https://mlsanity.com/paper/2504.01807/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 10 of 10)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes](https://mlsanity.com/paper/2010.05818/) (2020)
- [Control Barriers in Bayesian Learning of System Dynamics](https://mlsanity.com/paper/2012.14964/) (2020)
- [Data-driven verification and synthesis of stochastic systems via barrier certificates](https://mlsanity.com/paper/2111.10330/) (2021)
- [The cost of using exact confidence intervals for a binomial proportion](https://mlsanity.com/paper/1303.1288/) (2013)
- [Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions](https://mlsanity.com/paper/1903.07823/) (2019)
- [Safety Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2004.01821/) (2020)
- [Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States](https://mlsanity.com/paper/2303.17963/) (2023)
- [SOS Construction of Compatible Control Lyapunov and Barrier Functions](https://mlsanity.com/paper/2305.01222/) (2023)
- [Learning-based Parameterized Barrier Function for Safety-Critical Control of Unknown Systems](https://mlsanity.com/paper/2408.05319/) (2024)

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

- [Learning Dynamics from Infrequent Output Measurements for Uncertainty-Aware Optimal Control](https://mlsanity.com/paper/2512.08013/) (2025)

## Abstract (arXiv)

Certifying safety in dynamical systems is crucial, but barrier certificates - widely used to verify that system trajectories remain within a safe region - typically require explicit system models. When dynamics are unknown, data-driven methods can be used instead, yet obtaining a valid certificate requires rigorous uncertainty quantification. For this purpose, existing methods usually rely on full-state measurements, limiting their applicability. This paper proposes a novel approach for synthesizing barrier certificates for unknown systems with latent states and polynomial dynamics. A Bayesian framework is employed, where a prior in state-space representation is updated using output data via a targeted marginal Metropolis-Hastings sampler. The resulting samples are used to construct a barrier certificate through a sum-of-squares program. Probabilistic guarantees for its validity with respect to the true, unknown system are obtained by testing on an additional set of posterior samples. The approach and its probabilistic guarantees are illustrated through a numerical simulation.