Dynamical modeling and optimal control of landfills

We propose a simple model of landfill and study a minimal time control problem where the re-circulation leachate is the manipulated variable. We propose a scheme to construct the optimal strategy by dividing the state space into three subsets [Formula: see text], [Formula: see text] and the complementary. On [Formula: see text] and [Formula: see text], the optimal control is constant until reaching target, while it can exhibit a singular arc outside these two subsets. Moreover, the singular arc could have a barrier. In this case, we prove the existence of a switching curve that passes through a point of prior saturation under the assumption that the set [Formula: see text] intersects the singular arc. Numerical computations allow then to determine the switching curve and depict the optimal synthesis.