An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum
2016 (English)In: 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas: IEEE conference proceedings, 2016, 6477-6484 p.Conference paper (Refereed)
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
Las Vegas: IEEE conference proceedings, 2016. 6477-6484 p.
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
Other Mechanical Engineering
IdentifiersURN: urn:nbn:se:kth:diva-203285DOI: 10.1109/CDC.2016.7799266ScopusID: 2-s2.0-85010788244OAI: oai:DiVA.org:kth-203285DiVA: diva2:1081955
2016 IEEE 55th Conference on Decision and Control (CDC)
QC 201703212017-03-152017-03-152017-03-21Bibliographically approved