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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2015

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

Résumé

This paper is devoted to the study of an optimal control problem under the presence of a saturation point on the singular locus. We consider the minimal time problem for a system describing a fed-batch reactor with one species and one substrate. Our aim is to find an optimal feedback control that steers the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc. Unlike other studies on the minimal time problem governed by affine systems w.r.t. the control, we assume that the singular arc is non-necessary controllable everywhere. This brings interesting issues in terms of optimal synthesis. Thanks Pontryagin's Principle and numerical simulations, we provide an optimal synthesis of the problem.
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Dates et versions

hal-00879385 , version 1 (03-11-2013)
hal-00879385 , version 2 (05-08-2014)

Identifiants

Citer

Térence Bayen, Marc Mazade, Francis Mairet. Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc. Discrete and Continuous Dynamical Systems - Series B, 2015, 20 (1), pp.39-58. ⟨10.3934/dcdsb.2015.20.39⟩. ⟨hal-00879385v2⟩
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