# Neural Certificates for Safe Control Policies

arXiv: https://arxiv.org/abs/2006.08465 · HTML: https://mlsanity.com/paper/2006.08465/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 30 of 35)

- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Empowering Autonomous Driving with Large Language Models: A Safety Perspective](https://mlsanity.com/paper/2312.00812/) (2023)
- [Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.07695/) (2021)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation](https://mlsanity.com/paper/2404.07956/) (2024)
- [Learning Control Policies for Stochastic Systems with Reach-avoid Guarantees](https://mlsanity.com/paper/2210.05308/) (2022)
- [Safety Certification for Stochastic Systems via Neural Barrier Functions](https://mlsanity.com/paper/2206.01463/) (2022)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States](https://mlsanity.com/paper/2301.12012/) (2023)
- [Learning Robust Hybrid Control Barrier Functions for Uncertain Systems](https://mlsanity.com/paper/2101.06492/) (2021)
- [Reinforcement Learning for Safe Robot Control using Control Lyapunov Barrier Functions](https://mlsanity.com/paper/2305.09793/) (2023)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [Neural Koopman Lyapunov Control](https://mlsanity.com/paper/2201.05098/) (2022)
- [Joint Differentiable Optimization and Verification for Certified Reinforcement Learning](https://mlsanity.com/paper/2201.12243/) (2022)
- [On the Forward Invariance of Neural ODEs](https://mlsanity.com/paper/2210.04763/) (2022)
- [Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2203.02401/) (2022)
- [Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance](https://mlsanity.com/paper/2307.03015/) (2023)
- [Actor-Critic Physics-informed Neural Lyapunov Control](https://mlsanity.com/paper/2403.08448/) (2024)
- [Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees](https://mlsanity.com/paper/2403.07308/) (2024)
- [Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systems](https://mlsanity.com/paper/2210.08339/) (2022)
- [A General Framework for Verification and Control of Dynamical Models via Certificate Synthesis](https://mlsanity.com/paper/2309.06090/) (2023)
- [KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2206.01704/) (2022)
- [Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems](https://mlsanity.com/paper/2210.05304/) (2022)
- [Safe Reach Set Computation via Neural Barrier Certificates](https://mlsanity.com/paper/2404.18813/) (2024)
- [FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs](https://mlsanity.com/paper/2210.16940/) (2022)
- [Certified Training with Branch-and-Bound for Lyapunov-stable Neural Control](https://mlsanity.com/paper/2411.18235/) (2024)
- [Adversarially Robust Stability Certificates can be Sample-Efficient](https://mlsanity.com/paper/2112.10690/) (2021)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems](https://mlsanity.com/paper/2312.15340/) (2023)
- [A Policy Optimization Method Towards Optimal-time Stability](https://mlsanity.com/paper/2301.00521/) (2023)

## Abstract (arXiv)

This paper develops an approach to learn a policy of a dynamical system that is guaranteed to be both provably safe and goal-reaching. Here, the safety means that a policy must not drive the state of the system to any unsafe region, while the goal-reaching requires the trajectory of the controlled system asymptotically converges to a goal region (a generalization of stability). We obtain the safe and goal-reaching policy by jointly learning two additional certificate functions: a barrier function that guarantees the safety and a developed Lyapunov-like function to fulfill the goal-reaching requirement, both of which are represented by neural networks. We show the effectiveness of the method to learn both safe and goal-reaching policies on various systems, including pendulums, cart-poles, and UAVs.