---
res:
bibo_abstract:
- "In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis
has also fueled the development of Koopman operator-based control\r\nframeworks.
In order to preserve the relatively low data requirements for an\r\napproximation
via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed
in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical
systems can be realized by means of switched systems\r\ntechniques, using only
a finite set of autonomous Koopman operator-based\r\nreduced models. These individual
systems can be approximated very efficiently\r\nfrom data. The main idea is to
transform a control system into a set of\r\nautonomous systems for which the optimal
switching sequence has to be computed.\r\nIn this article, we extend these results
to continuous control inputs using\r\nrelaxation. This way, we combine the advantages
of the data efficiency of\r\napproximating a finite set of autonomous systems
with continuous controls. We\r\nshow that when using the Koopman generator, this
relaxation --- realized by\r\nlinear interpolation between two operators --- does
not introduce any error for\r\ncontrol affine systems. This allows us to control
high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate
models. The efficiency of the\r\nproposed approach is demonstrated using several
examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic
fluidic pinball.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sebastian
foaf_name: Peitz, Sebastian
foaf_surname: Peitz
foaf_workInfoHomepage: http://www.librecat.org/personId=47427
orcid: 0000-0002-3389-793X
- foaf_Person:
foaf_givenName: Samuel E.
foaf_name: Otto, Samuel E.
foaf_surname: Otto
- foaf_Person:
foaf_givenName: Clarence W.
foaf_name: Rowley, Clarence W.
foaf_surname: Rowley
bibo_doi: 10.1137/20M1325678
bibo_issue: '3'
bibo_volume: 19
dct_date: 2020^xs_gYear
dct_language: eng
dct_title: Data-Driven Model Predictive Control using Interpolated Koopman Generators@
...