The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes

Antonios Armaou, Ioannis G. Kevrekidis, Constantinos Theodoropoulos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present an equation-free multiscale computational framework for the design of "coarse" controllers for spatially distributed processes described by microscopic/mesoscopic evolution rules. In particular, we exploit the smoothness in space of the process observables to estimate the unknown coarse system dynamics. This is accomplished through appropriately initialized and linked ensembles of microscopic simulations realizing only a small portion of the macroscopic spatial domain (the so-called gaptooth and patch-dynamics schemes, [10]). We illustrate this framework by designing discrete-time, coarse linear controllers for a Lattice-Boltzmann (LB) scheme modelling a reaction-diffusion process (a kinetic-theory based realization of the FitzHugh-Nagumo equation in one spatial dimension).

Original languageEnglish (US)
Title of host publicationProceedings of the 2004 American Control Conference (AAC)
Pages926-932
Number of pages7
DOIs
StatePublished - Nov 29 2004
EventProceedings of the 2004 American Control Conference (AAC) - Boston, MA, United States
Duration: Jun 30 2004Jul 2 2004

Publication series

NameProceedings of the American Control Conference
Volume1
ISSN (Print)0743-1619

Other

OtherProceedings of the 2004 American Control Conference (AAC)
CountryUnited States
CityBoston, MA
Period6/30/047/2/04

Fingerprint

Controllers
Kinetic theory
Dynamical systems

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Armaou, A., Kevrekidis, I. G., & Theodoropoulos, C. (2004). The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes. In Proceedings of the 2004 American Control Conference (AAC) (pp. 926-932). (Proceedings of the American Control Conference; Vol. 1). https://doi.org/10.1109/ACC.2004.182368
Armaou, Antonios ; Kevrekidis, Ioannis G. ; Theodoropoulos, Constantinos. / The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes. Proceedings of the 2004 American Control Conference (AAC). 2004. pp. 926-932 (Proceedings of the American Control Conference).
@inproceedings{f4b824218b0543b0ae2fc2e178cf8865,
title = "The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes",
abstract = "We present an equation-free multiscale computational framework for the design of {"}coarse{"} controllers for spatially distributed processes described by microscopic/mesoscopic evolution rules. In particular, we exploit the smoothness in space of the process observables to estimate the unknown coarse system dynamics. This is accomplished through appropriately initialized and linked ensembles of microscopic simulations realizing only a small portion of the macroscopic spatial domain (the so-called gaptooth and patch-dynamics schemes, [10]). We illustrate this framework by designing discrete-time, coarse linear controllers for a Lattice-Boltzmann (LB) scheme modelling a reaction-diffusion process (a kinetic-theory based realization of the FitzHugh-Nagumo equation in one spatial dimension).",
author = "Antonios Armaou and Kevrekidis, {Ioannis G.} and Constantinos Theodoropoulos",
year = "2004",
month = "11",
day = "29",
doi = "10.1109/ACC.2004.182368",
language = "English (US)",
isbn = "0780383354",
series = "Proceedings of the American Control Conference",
pages = "926--932",
booktitle = "Proceedings of the 2004 American Control Conference (AAC)",

}

Armaou, A, Kevrekidis, IG & Theodoropoulos, C 2004, The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes. in Proceedings of the 2004 American Control Conference (AAC). Proceedings of the American Control Conference, vol. 1, pp. 926-932, Proceedings of the 2004 American Control Conference (AAC), Boston, MA, United States, 6/30/04. https://doi.org/10.1109/ACC.2004.182368

The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes. / Armaou, Antonios; Kevrekidis, Ioannis G.; Theodoropoulos, Constantinos.

Proceedings of the 2004 American Control Conference (AAC). 2004. p. 926-932 (Proceedings of the American Control Conference; Vol. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes

AU - Armaou, Antonios

AU - Kevrekidis, Ioannis G.

AU - Theodoropoulos, Constantinos

PY - 2004/11/29

Y1 - 2004/11/29

N2 - We present an equation-free multiscale computational framework for the design of "coarse" controllers for spatially distributed processes described by microscopic/mesoscopic evolution rules. In particular, we exploit the smoothness in space of the process observables to estimate the unknown coarse system dynamics. This is accomplished through appropriately initialized and linked ensembles of microscopic simulations realizing only a small portion of the macroscopic spatial domain (the so-called gaptooth and patch-dynamics schemes, [10]). We illustrate this framework by designing discrete-time, coarse linear controllers for a Lattice-Boltzmann (LB) scheme modelling a reaction-diffusion process (a kinetic-theory based realization of the FitzHugh-Nagumo equation in one spatial dimension).

AB - We present an equation-free multiscale computational framework for the design of "coarse" controllers for spatially distributed processes described by microscopic/mesoscopic evolution rules. In particular, we exploit the smoothness in space of the process observables to estimate the unknown coarse system dynamics. This is accomplished through appropriately initialized and linked ensembles of microscopic simulations realizing only a small portion of the macroscopic spatial domain (the so-called gaptooth and patch-dynamics schemes, [10]). We illustrate this framework by designing discrete-time, coarse linear controllers for a Lattice-Boltzmann (LB) scheme modelling a reaction-diffusion process (a kinetic-theory based realization of the FitzHugh-Nagumo equation in one spatial dimension).

UR - http://www.scopus.com/inward/record.url?scp=8744314145&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=8744314145&partnerID=8YFLogxK

U2 - 10.1109/ACC.2004.182368

DO - 10.1109/ACC.2004.182368

M3 - Conference contribution

AN - SCOPUS:8744314145

SN - 0780383354

T3 - Proceedings of the American Control Conference

SP - 926

EP - 932

BT - Proceedings of the 2004 American Control Conference (AAC)

ER -

Armaou A, Kevrekidis IG, Theodoropoulos C. The gaptooth scheme, patch dynamics and equation-free controller design for distributed complex/ multiscale processes. In Proceedings of the 2004 American Control Conference (AAC). 2004. p. 926-932. (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2004.182368