We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of, at least, an optimal solution. Then we present a detailed derivation of a first order optimality condition (involving the corresponding adjoint systems) characterizing these optimal solutions. Finally, a numerical example is shown.
Mots-clés : time optimal control, partial differential equations, optimality conditions, existence, bioreactor
@article{COCV_2011__17_3_722_0,
author = {Alvarez-V\'azquez, Lino J. and Fern\'andez, Francisco J. and Mart{\'\i}nez, Aurea},
title = {Analysis of a time optimal control problem related to the management of a bioreactor},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {722--748},
publisher = {EDP-Sciences},
volume = {17},
number = {3},
year = {2011},
doi = {10.1051/cocv/2010020},
mrnumber = {2826977},
zbl = {1230.49002},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2010020/}
}
TY - JOUR AU - Alvarez-Vázquez, Lino J. AU - Fernández, Francisco J. AU - Martínez, Aurea TI - Analysis of a time optimal control problem related to the management of a bioreactor JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 722 EP - 748 VL - 17 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2010020/ DO - 10.1051/cocv/2010020 LA - en ID - COCV_2011__17_3_722_0 ER -
%0 Journal Article %A Alvarez-Vázquez, Lino J. %A Fernández, Francisco J. %A Martínez, Aurea %T Analysis of a time optimal control problem related to the management of a bioreactor %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 722-748 %V 17 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2010020/ %R 10.1051/cocv/2010020 %G en %F COCV_2011__17_3_722_0
Alvarez-Vázquez, Lino J.; Fernández, Francisco J.; Martínez, Aurea. Analysis of a time optimal control problem related to the management of a bioreactor. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 722-748. doi : 10.1051/cocv/2010020. http://archive.numdam.org/articles/10.1051/cocv/2010020/
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