Time-optimal control of concentration changes in the chemostat with one single species

Abstract

• Control of bioprocesses with applications in wastewater treatment. • Modeling of a chemostat system including a recirculation parameter for the biomass. • Synthetize optimal feedback control laws based on singular strategies. • Singular strategies represent a trade-off in comparison with bang-bang trajectories. • Characterize robust control laws that can be implemented easily for a practitioner. We consider the problem of driving in minimal time a system describing a chemostat model to a target point. This problem finds applications typically in the case where the input substrate concentration changes yielding in a new steady state. One essential feature is that the system takes into account a recirculation of biomass effect. We depict an optimal synthesis and provide an optimal feedback control of the problem by using Pontryagin’s Principle and geometric control theory for a large class of kinetics.