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

Antonios Armaou; Ioannis G. Kevrekidis; Constantinos Theodoropoulos

doi:10.1109/ACC.2004.182368

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

Antonios Armaou, Ioannis G. Kevrekidis, Constantinos Theodoropoulos

Chemical & Biological Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Proceedings of the 2004 American Control Conference (AAC)
Pages	926-932
Number of pages	7
DOIs	https://doi.org/10.1109/ACC.2004.182368
State	Published - 2004
Event	Proceedings of the 2004 American Control Conference (AAC) - Boston, MA, United States Duration: Jun 30 2004 → Jul 2 2004

Publication series

Name	Proceedings of the American Control Conference
Volume	1
ISSN (Print)	0743-1619

Other

Other	Proceedings of the 2004 American Control Conference (AAC)
Country/Territory	United States
City	Boston, MA
Period	6/30/04 → 7/2/04

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

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10.1109/ACC.2004.182368

Cite this

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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",

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)",

note = "Proceedings of the 2004 American Control Conference (AAC) ; Conference date: 30-06-2004 Through 02-07-2004",

}

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 proceeding › Conference 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

Y1 - 2004

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).

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DO - 10.1109/ACC.2004.182368

M3 - Conference contribution

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SN - 0780383354

T3 - Proceedings of the American Control Conference

SP - 926

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

T2 - Proceedings of the 2004 American Control Conference (AAC)

Y2 - 30 June 2004 through 2 July 2004

ER -

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

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