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

• 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.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Annan maskinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Other Mechanical Engineering (hsv//eng)

Keyword

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

Publication and Content Type

ref (subject category)

kon (subject category)