Fed-batch bioreactor with mortality rate

We address the problem of finding an optimal feedback control for feeding a fed-batch bioreactor with one species and one substrate, from a given initial condition to a given target value in a minimal amount of time. Mortality rate for the biomass and nutrient recycling are taken into account in this work. The optimal synthesis (optimal feeding strategy) has been obtained by Moreno in 1999 when both mortality and recycling are considered negligible, in the case of Monod and Haldane growth function. Our objective is to study the effect of mortality and recycling on the optimal synthesis. We provide an optimal synthesis of the problem using Pontryagin maximum principle, which extends the result of Moreno in the impulsive framework with mortality and recycling effect.