Occupation Kernels and Densely Defined Liouville Operators for System Identification

Joel A. Rosenfeld; Rushikesh Kamalapurkar; Benjamin Russo; Taylor T. Johnson

doi:10.1109/CDC40024.2019.9029337

Occupation Kernels and Densely Defined Liouville Operators for System Identification

Joel A. Rosenfeld, Rushikesh Kamalapurkar, Benjamin Russo, Taylor T. Johnson

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

17 Scopus citations

Abstract

This manuscript introduces the concept of Liouville operators and occupation kernels over reproducing kernel Hilbert spaces (RKHSs). The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. These tools are then turned toward the problem of system identification where an inner product formula is developed to provide constraints on the parameters in a system identification setting. This system identification routine is validated through several numerical experiments, where each experiment examines various contributions to the parameter identification error via numerical integration methods and parameters for the kernel functions themselves.

Original language	English
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6455-6460
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9029337
State	Published - Dec 2019
Externally published	Yes
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: Dec 11 2019 → Dec 13 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	12/11/19 → 12/13/19

Funding

*This research was supported by the Air Force Office of Scientific Research (AFOSR) under contract numbers FA9550-15-1-0258, FA9550-16-1-0246, and FA9550-18-1-0122, the Air Force Research Laboratory (AFRL) under contract number FA8651-19-2-0009, and the Office of Naval Research (ONR) under contract N00014-18-1-2184. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsoring agencies.

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10.1109/CDC40024.2019.9029337

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Rosenfeld, J. A., Kamalapurkar, R., Russo, B., & Johnson, T. T. (2019). Occupation Kernels and Densely Defined Liouville Operators for System Identification. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 6455-6460). Article 9029337 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029337

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title = "Occupation Kernels and Densely Defined Liouville Operators for System Identification",

abstract = "This manuscript introduces the concept of Liouville operators and occupation kernels over reproducing kernel Hilbert spaces (RKHSs). The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. These tools are then turned toward the problem of system identification where an inner product formula is developed to provide constraints on the parameters in a system identification setting. This system identification routine is validated through several numerical experiments, where each experiment examines various contributions to the parameter identification error via numerical integration methods and parameters for the kernel functions themselves.",

author = "Rosenfeld, {Joel A.} and Rushikesh Kamalapurkar and Benjamin Russo and Johnson, {Taylor T.}",

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year = "2019",

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doi = "10.1109/CDC40024.2019.9029337",

language = "English",

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Rosenfeld, JA, Kamalapurkar, R, Russo, B & Johnson, TT 2019, Occupation Kernels and Densely Defined Liouville Operators for System Identification. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9029337, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, Institute of Electrical and Electronics Engineers Inc., pp. 6455-6460, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 12/11/19. https://doi.org/10.1109/CDC40024.2019.9029337

Occupation Kernels and Densely Defined Liouville Operators for System Identification. / Rosenfeld, Joel A.; Kamalapurkar, Rushikesh; Russo, Benjamin et al.
2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 6455-6460 9029337 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - This manuscript introduces the concept of Liouville operators and occupation kernels over reproducing kernel Hilbert spaces (RKHSs). The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. These tools are then turned toward the problem of system identification where an inner product formula is developed to provide constraints on the parameters in a system identification setting. This system identification routine is validated through several numerical experiments, where each experiment examines various contributions to the parameter identification error via numerical integration methods and parameters for the kernel functions themselves.

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DO - 10.1109/CDC40024.2019.9029337

M3 - Conference contribution

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T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019

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Rosenfeld JA, Kamalapurkar R, Russo B, Johnson TT. Occupation Kernels and Densely Defined Liouville Operators for System Identification. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 6455-6460. 9029337. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC40024.2019.9029337

Occupation Kernels and Densely Defined Liouville Operators for System Identification

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