# Learning Safe Neural Network Controllers with Barrier Certificates

arXiv: https://arxiv.org/abs/2009.09826 · HTML: https://mlsanity.com/paper/2009.09826/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2020.

## Built on by (most cited first, 18 of 18)

- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [On the Forward Invariance of Neural ODEs](https://mlsanity.com/paper/2210.04763/) (2022)
- [Neural Abstractions](https://mlsanity.com/paper/2301.11683/) (2023)
- [Barrier Functions Inspired Reward Shaping for Reinforcement Learning](https://mlsanity.com/paper/2403.01410/) (2024)
- [Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2203.02401/) (2022)
- [A General Framework for Verification and Control of Dynamical Models via Certificate Synthesis](https://mlsanity.com/paper/2309.06090/) (2023)
- [Ablation Study of How Run Time Assurance Impacts the Training and Performance of Reinforcement Learning Agents](https://mlsanity.com/paper/2207.04117/) (2022)
- [Safe Reach Set Computation via Neural Barrier Certificates](https://mlsanity.com/paper/2404.18813/) (2024)
- [Certified Training with Branch-and-Bound for Lyapunov-stable Neural Control](https://mlsanity.com/paper/2411.18235/) (2024)
- [Estimating Control Barriers from Offline Data](https://mlsanity.com/paper/2503.10641/) (2025)
- [Toward Neural-Network-Guided Program Synthesis and Verification](https://mlsanity.com/paper/2103.09414/) (2021)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [ABNet: Attention BarrierNet for Safe and Scalable Robot Learning](https://mlsanity.com/paper/2406.13025/) (2024)
- [Risk-Bounded Multi-Agent Visual Navigation via Iterative Risk Allocation](https://mlsanity.com/paper/2509.08157/) (2025)
- [Space Processor Computation Time Analysis for Reinforcement Learning and Run Time Assurance Control Policies](https://mlsanity.com/paper/2405.06771/) (2024)
- [Safe Human Robot Navigation in Warehouse Scenario](https://mlsanity.com/paper/2503.21141/) (2025)

## Abstract (arXiv)

We provide a novel approach to synthesize controllers for nonlinear continuous dynamical systems with control against safety properties. The controllers are based on neural networks (NNs). To certify the safety property we utilize barrier functions, which are represented by NNs as well. We train the controller-NN and barrier-NN simultaneously, achieving a verification-in-the-loop synthesis. We provide a prototype tool nncontroller with a number of case studies. The experiment results confirm the feasibility and efficacy of our approach.