Minimal time control of fed-batch bioreactor with product inhibition

Abstract

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Optimal control of physical backwash strategy - towards the enhancement of membrane filtration process performance

“…This approach is known in the literature as a chattering control [24,25]. Notice that applying such an approximation strategy will necessarily degrade the control performances since, by definition, any control signal will be less effective than the optimal one.…”

Minimal time problem for a fed-batch bioreactor with a non admissible singular arc

“…The objective of this work is to study a minimal time control problem in the plane, that is n = 2 where the singular control is not always admissible i.e. (2) is not always satisfied. We consider a fed-batch bioreactor with one species and one substrate.…”

“…Our aim is to find an optimal feedback control that steers the system in minimal time to a given target where the substrate concentration is less than a prescribed value, see [11]. Finding an optimal feeding strategy can significantly increase the performance of the system and has 1 Université Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5,France. tbayen@math.univ-montp2.fr, mmazade@math.univ-montp2.fr 2 several advantages from a practical point of view (see e.g. [1], [2], [7], [8], [9], [11]).…”

“…Finding an optimal feeding strategy can significantly increase the performance of the system and has 1 Université Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5,France. tbayen@math.univ-montp2.fr, mmazade@math.univ-montp2.fr 2 several advantages from a practical point of view (see e.g. [1], [2], [7], [8], [9], [11]). Whenever the growth function is of Monod type, then one can prove that the optimal feeding strategy is bang-bang [11].…”

“…It follows that there exists a volume value above which singular extremal trajectories are no longer optimal. Whereas in [11], [2], [1], we suppose that the maximal volume value can be reached by the singular arc, there exists a volume value above which it is not possible to keep the substrate concentration equal tos in the system. The main issue of the paper is the following.…”