Reachable Set of a Control Model for Two-Step Wastewater Biotreatment

Resumo

We consider a mathematical model describing a two-step process of wastewater biotreatment. This is a four-dimensional nonlinear system of differential equations with a scalar constraint on the control. The Pontryagin maximum principle is applied to investigate the boundary of the reachable set in this system. Among the possible parameter values and initial conditions of the model, we identify those for which piecewise-constant controls corresponding to boundary points of the reachable set have at most one, two, and three switching points.