Factorially Switching Dynamic Mode Decomposition for Koopman Analysis of Time-Variant Systems

Naoya Takeishi, Takehisa Yairi, Yoshinobu Kawahara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The modal decomposition based on the spectra of the Koopman operator has gained much attention in various areas such as data science and optimal control, and dynamic mode decomposition (DMD) has been known as a data-driven method for this purpose. However, there is a fundamental limitation in DMD and most of its variants; these methods are based on the premise that the target system is time-invariant at least within the data at hand. In this work, we aim to compute DMD on time-varying dynamical systems. To this end, we propose a probabilistic model that has factorially switching dynamic modes. In the proposed model, which is based on probabilistic DMD, observation at each time is expressed using a subset of dynamic modes, and the activation of the dynamic modes varies over time. We present an approximate inference method using expectation propagation and demonstrate the modeling capability of the proposed method with numerical examples of temporally-local events and transient phenomena.

Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6402-6408
Number of pages7
ISBN (Electronic)9781538613955
DOIs
Publication statusPublished - Jan 18 2019
Externally publishedYes
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Decomposition
Decompose
Data-driven
Probabilistic Model
Activation
Time-varying
Dynamical systems
Optimal Control
Dynamical system
Chemical activation
Vary
Propagation
Numerical Examples
Target
Subset
Invariant
Operator
Modeling
Demonstrate
Model

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Takeishi, N., Yairi, T., & Kawahara, Y. (2019). Factorially Switching Dynamic Mode Decomposition for Koopman Analysis of Time-Variant Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 6402-6408). [8619846] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619846

Factorially Switching Dynamic Mode Decomposition for Koopman Analysis of Time-Variant Systems. / Takeishi, Naoya; Yairi, Takehisa; Kawahara, Yoshinobu.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 6402-6408 8619846 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Takeishi, N, Yairi, T & Kawahara, Y 2019, Factorially Switching Dynamic Mode Decomposition for Koopman Analysis of Time-Variant Systems. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619846, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 6402-6408, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619846
Takeishi N, Yairi T, Kawahara Y. Factorially Switching Dynamic Mode Decomposition for Koopman Analysis of Time-Variant Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 6402-6408. 8619846. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619846
Takeishi, Naoya ; Yairi, Takehisa ; Kawahara, Yoshinobu. / Factorially Switching Dynamic Mode Decomposition for Koopman Analysis of Time-Variant Systems. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 6402-6408 (Proceedings of the IEEE Conference on Decision and Control).
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