Utility of the Koopman Operator in Output Regulation of Disturbed Nonlinear Systems

Bart Kieboom; Maria Bartzioka; Matin Jafarian

doi:10.1109/cdc49753.2023.10383637

Utility of the Koopman Operator in Output Regulation of Disturbed Nonlinear Systems

Bart Kieboom, Maria Bartzioka, Matin Jafarian

Team Matin Jafarian

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show that for a class of nonlinear systems admitting a finite-dimensional Koopman representation, the problem is equivalent to a bilinear output regulation. We then prove that a linear dynamic output feedback controller, inspired by the linear output regulation framework, locally solves the original nonlinear problem. Numerical results validate our analysis.

Original language	English
Title of host publication	Proceedings of the 62nd IEEE Conference on Decision and Control (CDC 2023)
Publisher	IEEE
Pages	2616-2621
Number of pages	6
ISBN (Electronic)	979-8-3503-0124-3
DOIs	https://doi.org/10.1109/cdc49753.2023.10383637
Publication status	Published - 2023
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Country/Territory	Singapore
City	Singapore
Period	13/12/23 → 15/12/23

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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abstract = "This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show that for a class of nonlinear systems admitting a finite-dimensional Koopman representation, the problem is equivalent to a bilinear output regulation. We then prove that a linear dynamic output feedback controller, inspired by the linear output regulation framework, locally solves the original nonlinear problem. Numerical results validate our analysis.",

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AB - This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show that for a class of nonlinear systems admitting a finite-dimensional Koopman representation, the problem is equivalent to a bilinear output regulation. We then prove that a linear dynamic output feedback controller, inspired by the linear output regulation framework, locally solves the original nonlinear problem. Numerical results validate our analysis.

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ER -

Utility of the Koopman Operator in Output Regulation of Disturbed Nonlinear Systems

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