Analysis of an optimal control problem related to microorganisms selection

Abstract

In this work, we consider a minimal time control problem governed by a system describing a continuous bioreactor with one substrate, n ≥ 2 species, and a mutation factor. Our aim is to select in minimal time the fastest species i.e. the one for which the half saturation constant is the lowest. In the case of two species, the optimal feeding strategy consists of a most rapid approach to a singular arc (see Bayen et al. [2014]). The aim of this paper is to study the case of n ≥ 2 species. Thanks to the Pontryagin Maximum Principle, we provide a sub-optimal strategy based on a most rapid approach to a singular arc that depends on the initial condition.