Dynamical modelling and optimal control of landfills

TL;DR

This paper develops a simple dynamical model for landfills and formulates an optimal control problem to determine the best re-circulation strategy, analyzing the structure of optimal solutions including singular arcs and switching curves.

Contribution

It introduces a novel minimal time control framework for landfills, including a scheme to construct optimal strategies and analyze complex control behaviors like singular arcs and barriers.

Findings

Optimal control strategy characterized by constant and singular arcs.

Existence of a switching curve passing through a saturation point.

Numerical methods effectively determine the optimal synthesis.

Abstract

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 E0, Z1 and the complementary. On E0 and Z1, 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 E0 intersects the singular arc. Numerical computations allow then to determine the switching curve and depict the optimal synthesis.