Optimal control of a bioeconomic model applied to the recovery of household waste

An improved mathematical model describing the process of generating energy from household waste treatment is proposed and analyzed. It is a three-dimensional nonlinear system that illustrates the process of transforming household waste stored in a landfill into energy that flows to a user's network. More precisely, the state of the system describes at a broad scale a process of generating energy E by treating a quota of a waste stock x through K-valorization units that may also consume a part of the produced energy for their operation. Our main objective is to maximize the energy produced and transmitted to the user's network. In particular, we investigate the issue of determining an optimal investing strategy that monitors the deployment of treatment plants. Using Pontryagin's maximum principle (PMP), we characterize, over a fixed time-frame [0, T], the optimal investment that maximizes the produced energy while limiting the overall production costs. In addition, the efficiency of the suggested strategy is validated and illustrated throughout this work using a direct optimization method.