Converging outer approximations to global attractors using semidefinite programming

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355970" target="_blank" >RIV/68407700:21230/21:00355970 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.automatica.2021.109900" target="_blank" >https://doi.org/10.1016/j.automatica.2021.109900</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.automatica.2021.109900" target="_blank" >10.1016/j.automatica.2021.109900</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Converging outer approximations to global attractors using semidefinite programming

Popis výsledku v původním jazyce

This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of increasing size with guaranteed convergence to the global attractor. The approach taken follows an established line of reasoning, where we first characterize the global attractor via an infinite dimensional linear programming problem (LP) in the space of Borel measures. The dual to this LP is in the space of continuous functions and its feasible solutions provide guaranteed outer approximations to the global attractor. For systems with polynomial dynamics, a hierarchy of finite-dimensional sum-of-squares tightenings of the dual LP provides a sequence of outer approximations to the global attractor with guaranteed convergence in the sense of volume discrep-ancy tending to zero. The method is very simple to use and based purely on convex optimization. Numerical examples with the code available online demonstrate the method. (C) 2021 Published by Elsevier Ltd.

Název v anglickém jazyce

Converging outer approximations to global attractors using semidefinite programming

Popis výsledku anglicky

This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of increasing size with guaranteed convergence to the global attractor. The approach taken follows an established line of reasoning, where we first characterize the global attractor via an infinite dimensional linear programming problem (LP) in the space of Borel measures. The dual to this LP is in the space of continuous functions and its feasible solutions provide guaranteed outer approximations to the global attractor. For systems with polynomial dynamics, a hierarchy of finite-dimensional sum-of-squares tightenings of the dual LP provides a sequence of outer approximations to the global attractor with guaranteed convergence in the sense of volume discrep-ancy tending to zero. The method is very simple to use and based purely on convex optimization. Numerical examples with the code available online demonstrate the method. (C) 2021 Published by Elsevier Ltd.

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/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koncept Koopmanova operátoru pro řízení komplexních nelineárních dynamických systémů</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Automatica

ISSN

0005-1098

e-ISSN

1873-2836

Svazek periodika

134

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

9

Strana od-do

—

Kód UT WoS článku

000704345200004

EID výsledku v databázi Scopus

2-s2.0-85115406959