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An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum
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2016 (English)In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, 6477-6484 p., 7799266Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016. 6477-6484 p., 7799266
Keyword [en]
control system analysis, nonlinear dynamical systems, Koopman analysis, Koopman operator theory, event-triggered state resets, geometric perspective, hybrid automaton, hybrid pendulum analysis, nonsmooth dynamical systems, operator-theoretic viewpoint, Angular velocity, Automata, Damping, Eigenvalues and eigenfunctions, Orbits, Power system dynamics, Trajectory
National Category
Other Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-203285DOI: 10.1109/CDC.2016.7799266ISI: 000400048106110Scopus ID: 2-s2.0-85010788244ISBN: 9781509018376 (print)OAI: oai:DiVA.org:kth-203285DiVA: diva2:1081955
Conference
55th IEEE Conference on Decision and Control, CDC 2016, ARIA Resort and CasinoLas Vegas, United States, 12 December 2016 through 14 December 2016
Note

QC 20170321

Available from: 2017-03-15 Created: 2017-03-15 Last updated: 2017-06-09Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf