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

Govindarajan, Nithin ; Arbabi, Hassan ; Van Blargian, Louis ; Matchen, Timothy ; Tegling, Emma LU and Mezic, Igor (2016) 55th IEEE Conference on Decision and Control, CDC 2016 In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 p.6477-6484
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.

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author
; ; ; ; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2016 IEEE 55th Conference on Decision and Control, CDC 2016
series title
2016 IEEE 55th Conference on Decision and Control, CDC 2016
article number
7799266
pages
8 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
55th IEEE Conference on Decision and Control, CDC 2016
conference location
Las Vegas, United States
conference dates
2016-12-12 - 2016-12-14
external identifiers
  • scopus:85010788244
ISBN
9781509018376
DOI
10.1109/CDC.2016.7799266
language
English
LU publication?
no
additional info
Publisher Copyright: © 2016 IEEE.
id
62ce680f-147d-4162-b373-093029c5d9bc
date added to LUP
2021-11-24 09:56:29
date last changed
2022-02-02 01:37:14
@inproceedings{62ce680f-147d-4162-b373-093029c5d9bc,
  abstract     = {{<p>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.</p>}},
  author       = {{Govindarajan, Nithin and Arbabi, Hassan and Van Blargian, Louis and Matchen, Timothy and Tegling, Emma and Mezic, Igor}},
  booktitle    = {{2016 IEEE 55th Conference on Decision and Control, CDC 2016}},
  isbn         = {{9781509018376}},
  language     = {{eng}},
  month        = {{12}},
  pages        = {{6477--6484}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{2016 IEEE 55th Conference on Decision and Control, CDC 2016}},
  title        = {{An operator-theoretic viewpoint to non-smooth dynamical systems : Koopman analysis of a hybrid pendulum}},
  url          = {{http://dx.doi.org/10.1109/CDC.2016.7799266}},
  doi          = {{10.1109/CDC.2016.7799266}},
  year         = {{2016}},
}