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

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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
Pages (from-to)	926-932
Number of pages	6
Journal	Proceedings of the American Control Conference
Volume	1
DOIs	https://doi.org/10.1109/ACC.2004.182368
Publication status	Published - 2004

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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",

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journal = "Proceedings of the American Control Conference",

issn = "0743-1619",

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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).

U2 - 10.1109/ACC.2004.182368

DO - 10.1109/ACC.2004.182368

M3 - Article

SN - 0743-1619

VL - 1

SP - 926

EP - 932

JO - Proceedings of the American Control Conference

JF - Proceedings of the American Control Conference

ER -

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

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