Data-driven transformations that reformulate nonlinear systems in a linear framework have
the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics …

In this work, we explore finite-dimensional linear representations of nonlinear dynamical
systems by restricting the Koopman operator to an invariant subspace spanned by specially …

The Koopman operator allows for handling nonlinear systems through a globally linear
representation. In general, the operator is infinite-dimensional–necessitating finite …

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear
dynamical systems as it provides coordinate transformations to globally linearize the …

Identifying coordinate transformations that make strongly nonlinear dynamics approximately
linear has the potential to enable nonlinear prediction, estimation, and control using linear …

As an example of fruitful cross-fertilization between mathematics and engineering, nonlinear
control theory has attracted considerable effort driven by the need to understand, predict …

We derive a data-driven method for the approximation of the Koopman generator called
gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic …

Finding an embedding space for a linear approximation of a nonlinear dynamical system
enables efficient system identification and control synthesis. The Koopman operator theory …

This paper presents a novel learning framework to construct Koopman eigenfunctions for
unknown, nonlinear dynamics using data gathered from experiments. The learning …

This article presents a novel data-driven framework for constructing eigenfunctions of the
Koopman operator geared toward prediction and control. The method leverages the …