# Learning Stability Certificates from Data

arXiv: https://arxiv.org/abs/2008.05952 · HTML: https://mlsanity.com/paper/2008.05952/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2020.

## Built on by (most cited first, 30 of 45)

- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [TaSIL: Taylor Series Imitation Learning](https://mlsanity.com/paper/2205.14812/) (2022)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Steering Dialogue Dynamics for Robustness against Multi-turn Jailbreaking Attacks](https://mlsanity.com/paper/2503.00187/) (2025)
- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems](https://mlsanity.com/paper/2110.14296/) (2021)
- [Control-oriented meta-learning](https://mlsanity.com/paper/2204.06716/) (2022)
- [Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates](https://mlsanity.com/paper/2405.14058/) (2024)
- [Learning Robust Hybrid Control Barrier Functions for Uncertain Systems](https://mlsanity.com/paper/2101.06492/) (2021)
- [Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach](https://mlsanity.com/paper/2102.12668/) (2021)
- [Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems](https://mlsanity.com/paper/2104.08695/) (2021)
- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Neural Koopman Lyapunov Control](https://mlsanity.com/paper/2201.05098/) (2022)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [Nonparametric adaptive control and prediction: theory and randomized algorithms](https://mlsanity.com/paper/2106.03589/) (2021)
- [Actor-Critic Physics-informed Neural Lyapunov Control](https://mlsanity.com/paper/2403.08448/) (2024)
- [Safe Value Functions](https://mlsanity.com/paper/2105.12204/) (2021)
- [RNNs of RNNs: Recursive Construction of Stable Assemblies of Recurrent Neural Networks](https://mlsanity.com/paper/2106.08928/) (2021)
- [Data-Driven Control with Inherent Lyapunov Stability](https://mlsanity.com/paper/2303.03157/) (2023)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2206.01704/) (2022)
- [Learning Control-Oriented Dynamical Structure from Data](https://mlsanity.com/paper/2302.02529/) (2023)
- [LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers](https://mlsanity.com/paper/2604.05374/) (2026)
- [Learning Contraction Policies from Offline Data](https://mlsanity.com/paper/2112.05911/) (2021)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Transformer-Based Fault-Tolerant Control for Fixed-Wing UAVs Using Knowledge Distillation and In-Context Adaptation](https://mlsanity.com/paper/2411.02975/) (2024)

## Abstract (arXiv)

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error - the probability that a certificate will not certify a new, unseen trajectory - when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.