Geodesic
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

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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.

DOI : 10.1051/cocv/2010020
Classification : 35D05, 49J20, 93C20
Keywords: time optimal control, partial differential equations, optimality conditions, existence, bioreactor 
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     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},
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     zbl = {1230.49002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010020/}
}
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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

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