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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Formation of a nontrivial finite-time stable attractor in a class of polyhedral sweeping processes with periodic input
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-14736S" target="_blank" >GA20-14736S: Hysteresis modeling in mathematical engineering</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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