Analysis of a time optimal control problem related to the management of a bioreactor***

Lino J. Alvarez-Vázquez; Francisco J. Fernández; Aurea Martínez

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 3, page 722-748
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Alvarez-Vázquez, Lino J., Fernández, Francisco J., and Martínez, Aurea. "Analysis of a time optimal control problem related to the management of a bioreactor***." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 722-748. <http://eudml.org/doc/221924>.

@article{Alvarez2011,
abstract = { 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. },
author = {Alvarez-Vázquez, Lino J., Fernández, Francisco J., Martínez, Aurea},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Time optimal control; partial differential equations; optimality conditions; existence; bioreactor; time optimal control; optimality conditions},
language = {eng},
month = {8},
number = {3},
pages = {722-748},
publisher = {EDP Sciences},
title = {Analysis of a time optimal control problem related to the management of a bioreactor***},
url = {http://eudml.org/doc/221924},
volume = {17},
year = {2011},
}

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
DA - 2011/8//
PB - EDP Sciences
VL - 17
IS - 3
SP - 722
EP - 748
AB - 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.
LA - eng
KW - Time optimal control; partial differential equations; optimality conditions; existence; bioreactor; time optimal control; optimality conditions
UR - http://eudml.org/doc/221924
ER -

References

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