Learning Stable and Passive Neural Differential Equations
Systems and Control
2024-12-11 v2 Machine Learning
Systems and Control
Abstract
In this paper, we introduce a novel class of neural differential equation, which are intrinsically Lyapunov stable, exponentially stable or passive. We take a recently proposed Polyak Lojasiewicz network (PLNet) as an Lyapunov function and then parameterize the vector field as the descent directions of the Lyapunov function. The resulting models have a same structure as the general Hamiltonian dynamics, where the Hamiltonian is lower- and upper-bounded by quadratic functions. Moreover, it is also positive definite w.r.t. either a known or learnable equilibrium. We illustrate the effectiveness of the proposed model on a damped double pendulum system.
Cite
@article{arxiv.2404.12554,
title = {Learning Stable and Passive Neural Differential Equations},
author = {Jing Cheng and Ruigang Wang and Ian R. Manchester},
journal= {arXiv preprint arXiv:2404.12554},
year = {2024}
}