Introduction to the Koopman operator in systems and control theory

Alexandre Mauroy, Yoshihiko Susuki, Igor Mezić

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Résumé

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.
langue originaleAnglais
titreThe Koopman Operator in Systems and Control
Sous-titreConcepts, Methodologies, and Applications
rédacteurs en chefAlexandre Mauroy, Igor Mezic, Yoshihiko Susuki
EditeurSpringer
Chapitre1
Pages3-33
Nombre de pages30
ISBN (Electronique)978-3-030-35713-9
ISBN (imprimé)978-3-030-35712-2
Etat de la publicationPublié - 2020

Série de publications

NomLecture Notes in Control and Information Sciences
EditeurSpringer
Volume484
ISSN (imprimé)0170-8643

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  • Contient cette citation

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