Learning Stable Koopman Embeddings
Machine Learning
2021-10-14 v1 Systems and Control
Systems and Control
Abstract
In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that every discrete-time nonlinear contracting model can be learnt in our framework. Another significant merit of the proposed approach is that it allows for unconstrained optimization over the Koopman embedding and operator jointly while enforcing stability of the model, via a direct parameterization of stable linear systems, greatly simplifying the computations involved. We validate our method on a simulated system and analyze the advantages of our parameterization compared to alternatives.
Cite
@article{arxiv.2110.06509,
title = {Learning Stable Koopman Embeddings},
author = {Fletcher Fan and Bowen Yi and David Rye and Guodong Shi and Ian R. Manchester},
journal= {arXiv preprint arXiv:2110.06509},
year = {2021}
}