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Equation-free gaptooth-based controller design for distributed complex/multiscale processes
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DOI：10.1016/j.compchemeng.2004.09.005.png)
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Abstract
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We present and illustrate a systematic computational methodology for the design of linear coarse-grained controllers for a class of spatially distributed processes. The approach targets systems described by micro- or mesoscopic evolution rules, for which coarse-grained, macroscopic evolution equations are not explicitly available. In particular, we exploit the smoothness in space of the process coarse variables (observables) to estimate the unknown macroscopic system dynamics. This is accomplished through appropriately initialized and connected ensembles of micro/mesoscopic simulations realizing a relatively small portion of the macroscopic spatial domain (the so-called gaptooth scheme). Our illustrative example consists of designing discrete-time, coarse linear controllers for a Lattice-Boltzmann model of a reaction-diffusion process (a kinetic-theory based realization of the FitzHugh-Nagumo equation in one spatial dimension). (c) 2004 Elsevier Ltd. All rights reserved.
Keywords:
distributed parameter systems
equation-free
multiscale
coarse-graining
time-steppers
optimal control
gaptooth scheme
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