Ensemble approximations for constrained dynamical systems using Liouville equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Ensemble approximations for constrained dynamical systems using Liouville equation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Ensemble approximations for constrained dynamical systems using Liouville equation

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

—

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

Automatica

ISSN

0005-1098

e-ISSN

1873-2836

Svazek periodika

149

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

13

Strana od-do

—

Kód UT WoS článku

000921598700001

EID výsledku v databázi Scopus

2-s2.0-85145654785