mlsanityData to 14 Oct 2026

Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems

arXiv 2312.15340 ↗First posted 23 Dec 2023eess.SY cs.LG cs.SYcited by 2

Not on the map. Why?

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.

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

14 of 37 references.

References · 14

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  2. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  3. 2018Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learningcited by 276
  4. 2020Neural Lyapunov Controlcited by 142
  5. 2020Learning Stable Deep Dynamics Modelscited by 111
  6. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 88
  7. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 68
  8. 2021Lyapunov-stable neural-network controlcited by 66
  9. 2020Learning Stability Certificates from Datacited by 45
  10. 2020Neural Certificates for Safe Control Policiescited by 35
  11. 2018Natural Language to Structured Query Generation via Meta-Learningcited by 33
  12. 2021Meta-Adaptive Nonlinear Control: Theory and Algorithmscited by 23
2 more
  1. 2019Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systemscited by 19
  2. 2022Distributed Learning of Neural Lyapunov Functions for Large-Scale Networked Dissipative Systemscited by 2

Built on by

Cited by year

Citing papers per year: 2024: 1; 2025: 1.

2 papers.

  1. 2024Trading Devil RL: Backdoor attack via Stock market, Bayesian Optimization and Reinforcement Learningcited by 0
  2. 2025MSACL: Multi-Step Actor-Critic Learning with Lyapunov Certificates for Exponentially Stabilizing Controlcited by 0