Guaranteed value strategy for the optimal control of biogas production in continuous bio-reactors

Abstract

In this work, we revisit a problem of optimal control for the maximisation of biogas production in a continuous bioreactor, for which the analytical determination of the optimal synthesis is an open problem. We consider two kinds of growth rates: substrate dependent or substrate and biomass dependent. We propose a sub-optimal controller, as a most rapid approach path strategy, and moreover we provide guaranteed bounds for the unknown value function of the optimal control problem. This controller has the property of being a stationary state feedback for the substrate dependent case, even though the optimal control problem is with fixed finite terminal time.