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Dynamical modelling and optimal control of landfills

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 $\mathcal{E}_0$, $\mathcal{Z}_{1}$ and the complementary. On $\mathcal{E}_0$ and $\mathcal{Z}_{1}$, 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 {\em barrier}. In this case, we prove the existence of a switching curve that passes through a point of {\em prior saturation} under the assumption that the set $\mathcal{E}_0$ intersects the singular arc. Numerical computations allow then to determine the switching curve and depict the optimal synthesis.
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Submitted on : Wednesday, May 27, 2020 - 11:06:34 AM
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Alain Rapaport, Térence Bayen, Matthieu Sebbah, Andres Donoso-Bravo, Alfredo Torrico. Dynamical modelling and optimal control of landfills. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2016, 26 (5), pp.901-929. ⟨10.1142/S0218202516500214⟩. ⟨hal-01087946v2⟩

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