An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum

Nithin Govindarajan; Hassan Arbabi; Louis Van Blargian; Timothy Matchen; Emma Tegling; Igor Mezic

doi:10.1109/CDC.2016.7799266

An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum

Nithin Govindarajan, Hassan Arbabi, Louis Van Blargian, Timothy Matchen, Emma Tegling, Igor Mezic

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

Abstract

We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick at certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism of Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by establishing a link between the spectral properties of the Koopman operator and the geometric properties in the state-space.

Original language	English
Title of host publication	2016 IEEE 55th Conference on Decision and Control, CDC 2016
Publisher	IEEE - Institute of Electrical and Electronics Engineers Inc.
Pages	6477-6484
Number of pages	8
ISBN (Electronic)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7799266
Publication status	Published - 2016 Dec 27
Externally published	Yes
Event	55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: 2016 Dec 12 → 2016 Dec 14

Publication series

Name	2016 IEEE 55th Conference on Decision and Control, CDC 2016

Conference

Conference	55th IEEE Conference on Decision and Control, CDC 2016
Country/Territory	United States
City	Las Vegas
Period	2016/12/12 → 2016/12/14

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Subject classification (UKÄ)

Control Engineering

Access to Document

10.1109/CDC.2016.7799266

Cite this

Govindarajan, N., Arbabi, H., Van Blargian, L., Matchen, T., Tegling, E., & Mezic, I. (2016). An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 6477-6484). Article 7799266 (2016 IEEE 55th Conference on Decision and Control, CDC 2016). IEEE - Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7799266

Govindarajan, Nithin ; Arbabi, Hassan ; Van Blargian, Louis et al. / An operator-theoretic viewpoint to non-smooth dynamical systems : Koopman analysis of a hybrid pendulum. 2016 IEEE 55th Conference on Decision and Control, CDC 2016. IEEE - Institute of Electrical and Electronics Engineers Inc., 2016. pp. 6477-6484 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).

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title = "An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum",

abstract = "We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick at certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism of Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by establishing a link between the spectral properties of the Koopman operator and the geometric properties in the state-space.",

author = "Nithin Govindarajan and Hassan Arbabi and {Van Blargian}, Louis and Timothy Matchen and Emma Tegling and Igor Mezic",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 55th IEEE Conference on Decision and Control, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",

year = "2016",

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doi = "10.1109/CDC.2016.7799266",

language = "English",

series = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

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Govindarajan, N, Arbabi, H, Van Blargian, L, Matchen, T, Tegling, E & Mezic, I 2016, An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7799266, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, IEEE - Institute of Electrical and Electronics Engineers Inc., pp. 6477-6484, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 2016/12/12. https://doi.org/10.1109/CDC.2016.7799266

An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum. / Govindarajan, Nithin; Arbabi, Hassan; Van Blargian, Louis et al.
2016 IEEE 55th Conference on Decision and Control, CDC 2016. IEEE - Institute of Electrical and Electronics Engineers Inc., 2016. p. 6477-6484 7799266 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).

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

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Govindarajan N, Arbabi H, Van Blargian L, Matchen T, Tegling E, Mezic I. An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. IEEE - Institute of Electrical and Electronics Engineers Inc. 2016. p. 6477-6484. 7799266. (2016 IEEE 55th Conference on Decision and Control, CDC 2016). doi: 10.1109/CDC.2016.7799266

An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum

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