Introduction to the Koopman operator in Systems and Control

Alexandre Mauroy, Yoshihiko Susuki

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

Abstract

The Koopman operator is a linear, infinite-dimensional operator defined for a nonlinear dynamical system. Through this linear operator, we can exploit established linear techniques (e.g. linear algebra, function analysis, operator theory) to tackle a wide variety of nonlinear problems in systems and control. In this paper, we present some research challenges in Koopman operator approach to nonlinear systems theory and control. Our discussion begins with a review of the current status of this approach—definitions of the Koopman operators for systems without/with inputs. We then pose distinct problems on identification, structural analysis, controller design, and computation related to Koopman operator theory in nonlinear control systems.
Original languageEnglish
Title of host publicationProceedings of the SICE Conference
Pages59-63
Number of pages5
Publication statusPublished - Sep 2018

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Operator Theory
Operator
Nonlinear Control Systems
Nonlinear Dynamical Systems
Structural Analysis
Systems Theory
Linear algebra
Controller Design
Linear Operator
Nonlinear Problem
Nonlinear Systems
Distinct
Review

Cite this

Mauroy, A., & Susuki, Y. (2018). Introduction to the Koopman operator in Systems and Control. In Proceedings of the SICE Conference (pp. 59-63)
Mauroy, Alexandre ; Susuki, Yoshihiko. / Introduction to the Koopman operator in Systems and Control. Proceedings of the SICE Conference. 2018. pp. 59-63
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Mauroy, A & Susuki, Y 2018, Introduction to the Koopman operator in Systems and Control. in Proceedings of the SICE Conference. pp. 59-63.

Introduction to the Koopman operator in Systems and Control. / Mauroy, Alexandre; Susuki, Yoshihiko.

Proceedings of the SICE Conference. 2018. p. 59-63.

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

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N2 - The Koopman operator is a linear, infinite-dimensional operator defined for a nonlinear dynamical system. Through this linear operator, we can exploit established linear techniques (e.g. linear algebra, function analysis, operator theory) to tackle a wide variety of nonlinear problems in systems and control. In this paper, we present some research challenges in Koopman operator approach to nonlinear systems theory and control. Our discussion begins with a review of the current status of this approach—definitions of the Koopman operators for systems without/with inputs. We then pose distinct problems on identification, structural analysis, controller design, and computation related to Koopman operator theory in nonlinear control systems.

AB - The Koopman operator is a linear, infinite-dimensional operator defined for a nonlinear dynamical system. Through this linear operator, we can exploit established linear techniques (e.g. linear algebra, function analysis, operator theory) to tackle a wide variety of nonlinear problems in systems and control. In this paper, we present some research challenges in Koopman operator approach to nonlinear systems theory and control. Our discussion begins with a review of the current status of this approach—definitions of the Koopman operators for systems without/with inputs. We then pose distinct problems on identification, structural analysis, controller design, and computation related to Koopman operator theory in nonlinear control systems.

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BT - Proceedings of the SICE Conference

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Mauroy A, Susuki Y. Introduction to the Koopman operator in Systems and Control. In Proceedings of the SICE Conference. 2018. p. 59-63