Closed-loop control of a reaction-diffusion system
Optimization and Control
2011-09-22 v1 Systems and Control
Abstract
A system of a parabolic partial differential equation coupled with ordinary differential inclusions that arises from a closed-loop control problem for a thermodynamic process governed by the Allen-Cahn diffusion reaction model is studied. A feedback law for the closed-loop control is proposed and implemented in the case of a finite number of control devices located inside the process domain basing on the process dynamics observed at a finite number of measurement points. The existence of solutions to the discussed system of differential equations is proved with the use of a generalization of the Kakutani fixed point theorem.
Cite
@article{arxiv.1109.4530,
title = {Closed-loop control of a reaction-diffusion system},
author = {Grzegorz Dudziuk and Marek Niezgódka},
journal= {arXiv preprint arXiv:1109.4530},
year = {2011}
}