Introduction to the Koopman operator in systems and control theory

Alexandre Mauroy, Yoshihiko Susuki, Igor Mezić

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)

Abstract

The introductory chapter provides an overview of the Koopman operator framework. We present basic notion and definitions, including those related to the spectral properties of the operator. We also review numerical methods that are used to represent the operator on a finite-dimensional basis and to compute its spectral properties from data (DMD algorithm and Arnoldi-based methods). Finally, several extensions of the Koopman operator to input-ouput systems are reviewed.
Original languageEnglish
Title of host publicationThe Koopman Operator in Systems and Control
Subtitle of host publicationConcepts, Methodologies, and Applications
EditorsAlexandre Mauroy, Igor Mezic, Yoshihiko Susuki
PublisherSpringer
Chapter1
Pages3-33
Number of pages30
ISBN (Electronic)978-3-030-35713-9
ISBN (Print)978-3-030-35712-2
Publication statusPublished - 2020

Publication series

NameLecture Notes in Control and Information Sciences
PublisherSpringer
Volume484
ISSN (Print)0170-8643

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  • Cite this

    Mauroy, A., Susuki, Y., & Mezić, I. (2020). Introduction to the Koopman operator in systems and control theory. In A. Mauroy, I. Mezic, & Y. Susuki (Eds.), The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications (pp. 3-33). (Lecture Notes in Control and Information Sciences; Vol. 484). Springer.