Meta-Learning-Based Adaptive Stability Certificates for Dynamical
  Systems
Amit Jena Dileep Kalathil Le Xie
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.