English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper introduces a framework for solving time-autonomous nonlinearinfinite horizon optimal control problems, under the assumption that allminimizers satisfy Pontryagin's necessary optimality conditions. In detail, weuse methods from the field of symplectic geometry to analyze the eigenvalues ofa Koopman operator that lifts Pontryagin's differential equation into asuitably defined infinite dimensional symplectic space. This has the advantagethat methods from the field of spectral analysis can be used to characterizeglobally optimal control laws. A numerical method for constructing optimalfeedback laws for nonlinear systems is then obtained by computing theeigenvalues and eigenvectors of a matrix that is obtained by projecting thePontryagin-Koopman operator onto a finite dimensional space. We illustrate theeffectiveness of this approach by computing accurate approximations of theoptimal nonlinear feedback law for a Van der Pol control system, which cannotbe stabilized by a linear control law.

Towards Global Optimal Control via Koopman Lifts