Formation of a nontrivial finite-time stable attractor in a class of polyhedral sweeping processes with periodic input

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00578413" target="_blank" >RIV/67985840:_____/23:00578413 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1051/cocv/2023074" target="_blank" >https://doi.org/10.1051/cocv/2023074</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/cocv/2023074" target="_blank" >10.1051/cocv/2023074</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Formation of a nontrivial finite-time stable attractor in a class of polyhedral sweeping processes with periodic input

Popis výsledku v původním jazyce

We consider a differential inclusion known as a polyhedral sweeping process. The general sweeping process was introduced by J.-J. Moreau as a modeling framework for quasistatic deformations of elastoplastic bodies, and a polyhedral sweeping process is typically used to model stresses in a network of elastoplastic springs. Krejčí’s theorem states that a sweeping process with periodic input has a global attractor which consists of periodic solutions, and all such periodic solutions follow the same trajectory up to a parallel translation. We show that in the case of polyhedral sweeping process with periodic input the attractor has to be a convex polyhedron χ of a fixed shape. We provide examples of elastoplastic spring models leading to structurally stable situations where χ is a one- or two- dimensional polyhedron. In general, an attractor of a polyhedral sweeping process may be either exponentially stable or finite-time stable and the main result of the paper consists of sufficient conditions for finite-time stability of the attractor, with upper estimates for the settling time. The results have implications for the shakedown theory.

Název v anglickém jazyce

Formation of a nontrivial finite-time stable attractor in a class of polyhedral sweeping processes with periodic input

Popis výsledku anglicky

We consider a differential inclusion known as a polyhedral sweeping process. The general sweeping process was introduced by J.-J. Moreau as a modeling framework for quasistatic deformations of elastoplastic bodies, and a polyhedral sweeping process is typically used to model stresses in a network of elastoplastic springs. Krejčí’s theorem states that a sweeping process with periodic input has a global attractor which consists of periodic solutions, and all such periodic solutions follow the same trajectory up to a parallel translation. We show that in the case of polyhedral sweeping process with periodic input the attractor has to be a convex polyhedron χ of a fixed shape. We provide examples of elastoplastic spring models leading to structurally stable situations where χ is a one- or two- dimensional polyhedron. In general, an attractor of a polyhedral sweeping process may be either exponentially stable or finite-time stable and the main result of the paper consists of sufficient conditions for finite-time stability of the attractor, with upper estimates for the settling time. The results have implications for the shakedown theory.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-14736S" target="_blank" >GA20-14736S: Modelování hystereze v matematickém inženýrství</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

ESAIM-Control Optimisation and Calculus of Variations

ISSN

1292-8119

e-ISSN

1262-3377

Svazek periodika

29

Číslo periodika v rámci svazku

November

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

42

Strana od-do

84

Kód UT WoS článku

001103806100001

EID výsledku v databázi Scopus

2-s2.0-85178476921