no code implementations • 15 Mar 2024 • Jun Liu, Yiming Meng, Maxwell Fitzsimmons, Ruikun Zhou
In this paper, we describe a lightweight Python framework that provides integrated learning and verification of neural Lyapunov functions for stability analysis.
1 code implementation • 15 Mar 2024 • Jun Liu, Yiming Meng, Maxwell Fitzsimmons, Ruikun Zhou
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of dimensionality.
no code implementations • 15 Feb 2024 • Yiming Meng, Ruikun Zhou, Amartya Mukherjee, Maxwell Fitzsimmons, Christopher Song, Jun Liu
We provide a theoretical analysis of both algorithms in terms of convergence of neural approximations towards the true optimal solutions in a general setting.
no code implementations • 14 Dec 2023 • Jun Liu, Yiming Meng, Maxwell Fitzsimmons, Ruikun Zhou
We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions.
no code implementations • 9 Sep 2020 • Yiming Meng, Yinan Li, Maxwell Fitzsimmons, Jun Liu
While the converse Lyapunov-barrier theorems are not constructive, as with classical converse Lyapunov theorems, we believe that the unified necessary and sufficient conditions with a single Lyapunov-barrier function are of theoretical interest and can hopefully shed some light on computational approaches.
