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Time‐steppers and ‘coarse’ control of distributed microscopic processes
Author(s) -
Armaou Antonios,
I. Siettos Constantinos,
G. Kevrekidis Ioannis
Publication year - 2003
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.865
Subject(s) - mesoscopic physics , realization (probability) , jacobian matrix and determinant , computer science , lattice boltzmann methods , action (physics) , process (computing) , dimension (graph theory) , control theory (sociology) , controller (irrigation) , statistical physics , mathematics , physics , control (management) , artificial intelligence , mechanics , statistics , pure mathematics , quantum mechanics , agronomy , biology , operating system
We present an equation‐free multiscale computational framework for the design of ‘coarse’ controllers for complex spatially distributed processes described by microscopic/mesoscopic evolution rules. 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 dynamics in one spatial dimension). Short ‘bursts’ of appropriately initialized simulation of the LB model are used to extract the stationary states (stable and unstable) and to estimate the information required to design the coarse controller (e.g. the action of the coarse slow Jacobian of the process). Copyright © 2004 John Wiley & Sons, Ltd.