joint work with Alain Rapaport, Roux Sébastien, Nesrine Kalboussi
We study theoretically on a simple crop model the problem of optimizing the crop biomass at harvesting date, choosing the temporal distribution of water under the constraint of a total water volume available for the season. We show with the tools of the optimal control theory that the optimal solution may present a singular arc, under a lower water availability, which leads to a bang-singular-bang solution. This differs from the usual irrigation policies under water scarcity, which are bang-bang.
joint work with Gerard Olivar Tost, Ingrid M. Cholo
In this paper, we analyze the existence of an optimal resource control problem with an infinite time horizon of a system of differential equations with nonlinear dynamics and linear control. Our system of differential equations corresponds to a model of sustainable development. The variables in the state space are related to economics, ecosystems and social dimensions. We deal with the problem of non-convexity, and we prove the existence of optimal solutions, which are interpreted in the sustainable and economic environment.