Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc

Térence Bayen; Marc Mazade; Francis Mairet

doi:10.3934/dcdsb.2015.20.39

Article Contents

2015, Volume 20, Issue 1: 39-58. Doi: 10.3934/dcdsb.2015.20.39

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Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc

1.
Université Montpellier 2, CC 051, 34095 Montpellier cedex 5
2.
Inria 'BIOCORE' team, Inria Sophia-Antipolis, route des Lucioles, 06902 Sophia-Antipolis

Received: October 31, 2013

Revised: June 30, 2014

Published: December 2014

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Abstract

We study a minimal time control problem under the presence of a saturation point on the singular locus. The system describes a fed-batch reactor with one species and one substrate. Our aim is to find an optimal feedback control steering the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc which is non-necessary admissible everywhere (i.e. the singular control can take values outside the admissible control set). Thanks to Pontrygin's Principle, we provide an optimal synthesis of the problem that exhibits a frame point at the intersection of the singular arc and a switching curve. Numerical simulations allow to compute this curve and the frame point.

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Mathematics Subject Classification: Primary: 49J15, 49K15, 92B05; Secondary: 93C95.

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