Time-steppers and 'coarse' control of distributed microscopic processes

Antonios Armaou, Constantinos I. Siettos, Ioannis G. Kevrekidis

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Abstract

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).

Original languageEnglish (US)
Pages (from-to)89-111
Number of pages23
JournalInternational Journal of Robust and Nonlinear Control
Volume14
Issue number2
DOIs
StatePublished - Jan 24 2004

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All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Chemical Engineering(all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering

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