The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Physics is a field of science that has traditionally used the scientific method to answer
questions about why natural phenomena occur and to make testable models that explain the …

A common way to represent a system's dynamics is to specify how the state evolves in time.
An alternative viewpoint is to specify how functions of the state evolve in time. This evolution …

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 …

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

We develop a data-driven, model-free approach for the optimal control of the dynamical
system. The proposed approach relies on the Deep Neural Network (DNN) based learning …

This article presents a generalizable methodology for data-driven identification of nonlinear
dynamics that bounds the model error in terms of the prediction horizon and the magnitude …

The Koopman framework proposes a linear representation of finite-dimensional nonlinear
systems through a generally infinite-dimensional globally linear embedding. Originally, the …

Koopman operator theory has been gaining momentum for model extraction, planning, and
control of data-driven robotic systems. The Koopman operator's ability to extract dynamics …

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging
as a powerful modeling and learning-based control method enabling significant …