Mathematical modelling and optimal control strategies in biodegradation processes

Abstract We investigate the application of optimal control theory to waste management procedures, in particular to anaerobic degradation processes in bioreactor systems, to highlight how mathematical tools can inform decision-makers. Starting from a mathematical model describing the interactions among soluble substrate, insoluble substrate, and biomass, we formulate and analyze both finite-horizon and time optimal control problems in which leachate recirculation acts as the control variable. In the finite-horizon framework, optimal strategies are designed to balance substrate reduction and operational costs. In contrast, the time-optimal formulation aims to minimize the time required for the system to reach a prescribed target. Analytical insights derived from the application of Pontryagin Minimum Principle, complemented by numerical simulations, allow for the characterization of the optimal control and the analysis of the role played by the initial substrate composition, operational costs, and target shape on the resulting strategies.