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.

本文研究了神经网络在动态系统中的自适应稳定性认证问题，提出了与参数不确定性相关的神经李雅普诺夫函数的方法，通过与模型无关元学习的整合，提出了元神经李雅普诺夫函数，以应对参数变化带来的稳定性评估性能下降的问题。通过在标准基准自主动态系统上验证，证明了元神经李雅普诺夫函数在稳定性评估方面的性能。

元学习基于自适应稳定证书的动态系统