---
res:
bibo_abstract:
- We present a new framework for optimal and feedback control of PDEs using Koopman
operator-based reduced order models (K-ROMs). The Koopman operator is a linear
but infinite-dimensional operator which describes the dynamics of observables.
A numerical approximation of the Koopman operator therefore yields a linear system
for the observation of an autonomous dynamical system. In our approach, by introducing
a finite number of constant controls, the dynamic control system is transformed
into a set of autonomous systems and the corresponding optimal control problem
into a switching time optimization problem. This allows us to replace each of
these systems by a K-ROM which can be solved orders of magnitude faster. By this
approach, a nonlinear infinite-dimensional control problem is transformed into
a low-dimensional linear problem. Using a recent convergence result for the numerical
approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the
value of the K-ROM based objective function converges in measure to the value
of the full objective function. To illustrate the results, we consider the 1D
Burgers equation and the 2D Navierâ€“Stokes equations. The numerical experiments
show remarkable performance concerning both solution times and accuracy.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sebastian
foaf_name: Peitz, Sebastian
foaf_surname: Peitz
foaf_workInfoHomepage: http://www.librecat.org/personId=47427
orcid: https://orcid.org/0000-0002-3389-793X
- foaf_Person:
foaf_givenName: Stefan
foaf_name: Klus, Stefan
foaf_surname: Klus
bibo_doi: 10.1016/j.automatica.2019.05.016
bibo_volume: 106
dct_date: 2019^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0005-1098
dct_language: eng
dct_title: Koopman operator-based model reduction for switched-system control of
PDEs@
...