# Verification of safety critical control policies using kernel methods

arXiv: https://arxiv.org/abs/2203.12407 · HTML: https://mlsanity.com/paper/2203.12407/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 23 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Bayesian Controller Fusion: Leveraging Control Priors in Deep Reinforcement Learning for Robotics](https://mlsanity.com/paper/2107.09822/) (2021)
- [Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systems](https://mlsanity.com/paper/1611.00122/) (2016)
- [Multi-objective minimum time optimal control for low-thrust trajectory design](https://mlsanity.com/paper/2103.08813/) (2021)

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

- [Certified Approximate Reachability (CARe): Formal Error Bounds on Deep Learning of Reachable Sets](https://mlsanity.com/paper/2503.23912/) (2025)

## Abstract (arXiv)

Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example.