SET-VALUED KOOPMAN THEORY FOR CONTROL SYSTEMS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00387469" target="_blank" >RIV/68407700:21230/25:00387469 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/24M1633133" target="_blank" >https://doi.org/10.1137/24M1633133</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/24M1633133" target="_blank" >10.1137/24M1633133</a>

Jazyk výsledku

angličtina

Název v původním jazyce

SET-VALUED KOOPMAN THEORY FOR CONTROL SYSTEMS

Popis výsledku v původním jazyce

In this paper, we introduce a new notion of Koopman operator which faithfully encodes the dynamics of controlled systems by leveraging the tools of set-valued analysis. In this context, we propose generalizations of the Liouville and Perron--Frobenius operators and show that they respectively coincide with proper set-valued analogues of the infinitesimal generator and dual operator of the Koopman semigroup. We also give meaning to the spectra of these set-valued maps and prove an adapted version of the classical spectral mapping theorem relating the eigenvalues of a semigroup with those of its generator. Our approach provides theoretical justifications for existing practical methods in the Koopman community that study control systems by bundling together the Koopman and Liouville operators associated with different control inputs.

Název v anglickém jazyce

SET-VALUED KOOPMAN THEORY FOR CONTROL SYSTEMS

Popis výsledku anglicky

In this paper, we introduce a new notion of Koopman operator which faithfully encodes the dynamics of controlled systems by leveraging the tools of set-valued analysis. In this context, we propose generalizations of the Liouville and Perron--Frobenius operators and show that they respectively coincide with proper set-valued analogues of the infinitesimal generator and dual operator of the Koopman semigroup. We also give meaning to the spectra of these set-valued maps and prove an adapted version of the classical spectral mapping theorem relating the eigenvalues of a semigroup with those of its generator. Our approach provides theoretical justifications for existing practical methods in the Koopman community that study control systems by bundling together the Koopman and Liouville operators associated with different control inputs.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

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 Control and Optimization

ISSN

0363-0129

e-ISSN

1095-7138

Svazek periodika

63

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

3644-3673

Kód UT WoS článku

001592795600010

EID výsledku v databázi Scopus

2-s2.0-105023059267