Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems
It addresses stability certification for dynamical systems with time-varying parameters, an incremental improvement over existing neural Lyapunov methods.
This paper tackles the problem of neural network-based adaptive stability certification for dynamical systems under parametric uncertainty, proposing meta-NLFs that integrate meta-learning with neural Lyapunov functions to adapt to parameter shifts, and demonstrates improved performance on benchmark systems.
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.