Summary
International Symposium on Nonlinear Theory and Its Applications
2016
Session Number:B2L-B
Session:
Number:B2L-B-1
Koopman Operator Theory for Nonlinear Dynamical Systems: an Introduction with Engineering Applications
Yoshihiko Susuki, Igor Mezi?,
pp.-
Publication Date:2016/11/27
Online ISSN:2188-5079
Summary:
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 by the original nonlinear system. In particular, spectral properties of the Koopman operator play a crucial role in analyzing the original system. In the first part of this presentation, we review the so-called Koopman operator theory for nonlinear dynamical systems, with emphasis on modal decomposition and computation that are direct to wide applications. Then, in the second part, we present a series of applications of the Koopman operator theory to power and energy systems engineering. The applications are established as data-centric methods, namely, how to use massive quantities of data obtained numerically and experimentally, through spectral analysis of the Koopman operator.