# 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

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topAlvarez-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 -

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