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

Published online by Cambridge University Press:  23 April 2010

Lino J. Alvarez-Vázquez ,
Francisco J. Fernández  and
Aurea Martínez
Lino J. Alvarez-Vázquez
Affiliation:
Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación, Universidad de Vigo, 36310 Vigo, Spain. lino@dma.uvigo.es; aurea@dma.uvigo.es
Francisco J. Fernández
Affiliation:
Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15706 Santiago, Spain. fjavier.fernandez@usc.es
Aurea Martínez
Affiliation:
Departamento de Matemática Aplicada II, E.T.S.I. Telecomunicación, Universidad de Vigo, 36310 Vigo, Spain. lino@dma.uvigo.es; aurea@dma.uvigo.es
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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.

Keywords

Time optimal controlpartial differential equationsoptimality conditionsexistencebioreactor
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 3 , July 2011 , pp. 722 - 748
Copyright
© EDP Sciences, SMAI, 2010

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