An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum
Dynamical Systems
2016-09-01 v1
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 under certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism carried out by Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by means of establishing a link between the spectral properties of the Koopman operator and the geometric properties in the state-space.
Keywords
Cite
@article{arxiv.1608.08734,
title = {An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum},
author = {Nithin Govindarajan and Hassan Arbabi and Louis van Blargian and Timothy Matchen and Emma Tegling and Igor Mezić},
journal= {arXiv preprint arXiv:1608.08734},
year = {2016}
}