Closed-loop control of a reaction-diffusion system

Details Closed-loop control of a reaction-diffusion system Closed-loop control of a reaction-diffusion system

2011-09-21

arxiv.org/abs/1109.4530v1

Mathematics

Optimization and Control

Scientific paper

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.

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