Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation
Abstract
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to satisfy the negative orbital derivative condition, which only renders a single term in the empirical risk function in practice. This significantly reduces the number of hyper-parameters compared to existing methods. We also provide theoretical justifications on the approximation power of Lyapunov-Net and its complexity bounds. We demonstrate the efficiency of the proposed method on nonlinear dynamical systems involving up to 30-dimensional state spaces, and show that the proposed approach significantly outperforms the state-of-the-art methods.
Cite
@article{arxiv.2109.13359,
title = {Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation},
author = {Nathan Gaby and Fumin Zhang and Xiaojing Ye},
journal= {arXiv preprint arXiv:2109.13359},
year = {2022}
}
Comments
Accepted to 61st IEEE Conference on Decision and Control