Learning Parametric Koopman Decompositions for Prediction and Control
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00386385" target="_blank" >RIV/68407700:21230/25:00386385 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/23M1604576" target="_blank" >https://doi.org/10.1137/23M1604576</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/23M1604576" target="_blank" >10.1137/23M1604576</a>
Alternative languages
Result language
angličtina
Original language name
Learning Parametric Koopman Decompositions for Prediction and Control
Original language description
We present an approach to constructing approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of projected Koopman operators acting on this subspace. We parametrize both the projected Koopman operator family and the dictionary that spans the invariant subspace by neural networks, and jointly train them with trajectory data. We show theoretically the validity of our approach and demonstrate via numerical experiments that it exhibits significant improvements over existing methods in solving prediction problems, especially those with large state or parameter dimensions, and those possessing strongly nonlinear dynamics. Moreover, our method enables data-driven solution of optimal control problems involving nonlinear dynamics, with some interesting implications for controllability.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
<a href="/en/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotics and advanced industrial production</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Siam Journal on Applied Dynamical Systems
ISSN
1536-0040
e-ISSN
—
Volume of the periodical
24
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
38
Pages from-to
744-781
UT code for WoS article
001447232500010
EID of the result in the Scopus database
2-s2.0-105000160316