Applied Koopman Operator Theory for Power Systems Technology

2 Summarized theory of Koopman operators

Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described b...

Deep learning for universal linear embeddings of nonlinear dynamics

Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged as a leading data-driven embedding, as eigenfunctions of this operator provi...

On Matching, and Even Rectifying, Dynamical Systems through Koopman Operator Eigenfunctions

through Koopman Operator Eigenfunctions. Erik M. Bollt, a) Qianxiao Li, b) Felix Dietrich, c) and Ioannis Kevrekidis d) Department of Mathematics, Department of Electrical and Computer Engineering, Department of Physics, Clarkson University, Potsdam, New York 13699, USA Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore 138632, Singapore Department o...

Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting modelbased control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-dri...

Weighted Frobenius-Perron and Koopman operators