# Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems

arXiv: https://arxiv.org/abs/2312.15340 · HTML: https://mlsanity.com/paper/2312.15340/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 23 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions](https://mlsanity.com/paper/2004.07584/) (2020)
- [Lyapunov-stable neural-network control](https://mlsanity.com/paper/2109.14152/) (2021)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [Neural Certificates for Safe Control Policies](https://mlsanity.com/paper/2006.08465/) (2020)
- [Natural Language to Structured Query Generation via Meta-Learning](https://mlsanity.com/paper/1803.02400/) (2018)
- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems](https://mlsanity.com/paper/1903.01577/) (2019)
- [Distributed Learning of Neural Lyapunov Functions for Large-Scale Networked Dissipative Systems](https://mlsanity.com/paper/2207.07731/) (2022)

## Built on by (most cited first, 2 of 2)

- [Trading Devil RL: Backdoor attack via Stock market, Bayesian Optimization and Reinforcement Learning](https://mlsanity.com/paper/2412.17908/) (2024)
- [MSACL: Multi-Step Actor-Critic Learning with Lyapunov Certificates for Exponentially Stabilizing Control](https://mlsanity.com/paper/2512.24955/) (2025)

## Abstract (arXiv)

This paper addresses the problem of Neural Network (NN) based adaptive stability certification in a dynamical system. The state-of-the-art methods, such as Neural Lyapunov Functions (NLFs), use NN-based formulations to assess the stability of a non-linear dynamical system and compute a Region of Attraction (ROA) in the state space. However, under parametric uncertainty, if the values of system parameters vary over time, the NLF methods fail to adapt to such changes and may lead to conservative stability assessment performance. We circumvent this issue by integrating Model Agnostic Meta-learning (MAML) with NLFs and propose meta-NLFs. In this process, we train a meta-function that adapts to any parametric shifts and updates into an NLF for the system with new test-time parameter values. We demonstrate the stability assessment performance of meta-NLFs on some standard benchmark autonomous dynamical systems.