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/272765>.

@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},
language = {eng},
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/272765},
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
PY - 2011
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
UR - http://eudml.org/doc/272765
ER -

References

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