Ensemble approximations for constrained dynamical systems using Liouville equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00366128" target="_blank" >RIV/68407700:21230/23:00366128 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.automatica.2022.110836" target="_blank" >https://doi.org/10.1016/j.automatica.2022.110836</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.automatica.2022.110836" target="_blank" >10.1016/j.automatica.2022.110836</a>

Result language

angličtina

Original language name

Ensemble approximations for constrained dynamical systems using Liouville equation

Original language description

For a class of state-constrained dynamical systems described by evolution variational inequalities, we study the time evolution of a probability measure which describes the distribution of the state over a set. In contrast to smooth ordinary differential equations, where the evolution of this probability measure is described by the Liouville equations, the flow map associated with the nonsmooth differential inclusion is not necessarily invertible and one cannot directly derive a continuity equation to describe the evolution of the distribution of states. Instead, we consider Lipschitz approximation of our original nonsmooth system and construct a sequence of measures obtained from Liouville equations corresponding to these approximations. This sequence of measures converges in weak -star topology to the measure describing the evolution of the distribution of states for the original nonsmooth system. This allows us to approximate numerically the evolution of moments (up to some finite order) for our original nonsmooth system, using a solver that uses finite order moment approximations of the Liouville equation. Our approach is illustrated with the help of two academic examples. (c) 2023 Elsevier Ltd. All rights reserved.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

20205 - Automation and control systems

Project

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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

Name of the periodical

Automatica

ISSN

0005-1098

e-ISSN

1873-2836

Volume of the periodical

149

Issue of the periodical within the volume

March

Country of publishing house

GB - UNITED KINGDOM

Number of pages

13

Pages from-to

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UT code for WoS article

000921598700001

EID of the result in the Scopus database

2-s2.0-85145654785