Learning Parametric Koopman Decompositions for Prediction and Control

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Learning Parametric Koopman Decompositions for Prediction and Control

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Learning Parametric Koopman Decompositions for Prediction and Control

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

<a href="/cs/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotika a pokročilá průmyslová výroba</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Siam Journal on Applied Dynamical Systems

ISSN

1536-0040

e-ISSN

—

Svazek periodika

24

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

38

Strana od-do

744-781

Kód UT WoS článku

001447232500010

EID výsledku v databázi Scopus

2-s2.0-105000160316