Introduction to the Koopman operator in dynamical systems and control theory

Alexandre Mauroy; Yoshihiko Susuki; Igor Mezić

doi:10.1007/978-3-030-35713-9_1

Introduction to the Koopman operator in dynamical systems and control theory

Alexandre Mauroy, Yoshihiko Susuki, Igor Mezić

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Abstract

This introductory chapter provides an overview of the Koopman operator framework. We present basic notions 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–output systems are reviewed.

Original language	English
Title of host publication	The Koopman Operator in Systems and Control
Subtitle of host publication	Concepts, Methodologies, and Applications
Editors	Alexandre Mauroy, Igor Mezic, Yoshihiko Susuki
Publisher	Springer
Chapter	1
Pages	3-33
Number of pages	31
Volume	484
ISBN (Electronic)	978-3-030-35713-9
ISBN (Print)	978-3-030-35712-2
DOIs	https://doi.org/10.1007/978-3-030-35713-9_1
Publication status	Published - 2020

Publication series

Name	Lecture Notes in Control and Information Sciences
Publisher	Springer
Volume	484
ISSN (Print)	0170-8643

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10.1007/978-3-030-35713-9_1

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Mauroy, A., Susuki, Y., & Mezić, I. (2020). Introduction to the Koopman operator in dynamical systems and control theory. In A. Mauroy, I. Mezic, & Y. Susuki (Eds.), The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications (Vol. 484, pp. 3-33). (Lecture Notes in Control and Information Sciences; Vol. 484). Springer. https://doi.org/10.1007/978-3-030-35713-9_1

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Mauroy, A, Susuki, Y & Mezić, I 2020, Introduction to the Koopman operator in dynamical systems and control theory. in A Mauroy, I Mezic & Y Susuki (eds), The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications. vol. 484, Lecture Notes in Control and Information Sciences, vol. 484, Springer, pp. 3-33. https://doi.org/10.1007/978-3-030-35713-9_1

Introduction to the Koopman operator in dynamical systems and control theory. / Mauroy, Alexandre; Susuki, Yoshihiko; Mezić, Igor.
The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications. ed. / Alexandre Mauroy; Igor Mezic; Yoshihiko Susuki. Vol. 484 Springer, 2020. p. 3-33 (Lecture Notes in Control and Information Sciences; Vol. 484).

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

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Introduction to the Koopman operator in dynamical systems and control theory

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