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

Térence Bayen | Zendy; Marc Mazade | Zendy; Francis Mairet | Zendy

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

Author(s) -

Térence Bayen,

Marc Mazade,

Francis Mairet

Publication year - 2014

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2015.20.39

Subject(s) - mathematics , intersection (aeronautics) , singular control , control theory (sociology) , singular solution , singular point of a curve , arc length , optimal control , arc (geometry) , point (geometry) , frame (networking) , control (management) , mathematical analysis , mathematical optimization , computer science , geometry , engineering , telecommunications , artificial intelligence , aerospace engineering

International audienceThis 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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