Learning Stable Koopman Embeddings

TL;DR

This paper introduces a data-driven approach to learn stable nonlinear system models using Koopman embeddings, enabling unconstrained optimization and stability enforcement in a higher-dimensional linear space.

Contribution

It presents a novel method for learning stable Koopman embeddings that can model all discrete-time contracting nonlinear systems with simplified stability constraints.

Findings

Successfully applied to a simulated system

Demonstrates advantages over alternative parameterizations

Enforces stability through direct linear system parameterization

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.