Irrigation Optimization by Modeling of Plant-Soil Interaction

Abstract

Irrigation scheduling is an important issue for crop management, in a general context of limited water resources and increasing concern about agricultural productivity. Methods to optimize crop irrigation should take into account the impact of water stress on plant growth and the water balance in the plant-soil-atmosphere system. In this article, we propose a methodology to solve the irrigation scheduling problem. For this purpose, a plant-soil interaction model is used to simulate the structural-functional plant growth conditioned by water status. The system dynamics is driven by a delay differential system. By considering a price for the crop yield and for the water resource, an optimal control problem can be formulated in order to find the optimal irrigation strategy. The solution is obtained by dynamic programming. In order to handle the delay term of the system due to the continuous mechanism of plant senescence and the curse of dimensionality, the iterative approach of dynamic programming is used.

Optimal control of a crop irrigation model under water scarcity

“…that defines the quota mentioned in the introduction. Then, the determination of the maximal biomass production is stated as the optimal control problem sup B(T ), u(•) ∈ U that satisfies (12) .…”

“…Consider any S(•) solution of ( 2),( 4) for an admissible control u(•) satisfying the constraint (12). Notice first that the set…”

“…Consider now a solution S(•), B(•) with an admissible control u(•) that is null on [0, t] and satisfies the constraint (12), and the set…”

“…which satisfies also the constraint (12). Denote S # (•), B # (•) the solution with the control u # (•).…”

“…Numerous texts and articles have developed systematic approaches to tackle the scheduling optimization problem. We refer to [11,12,18,19,23] and references therein. However, most of the existing approaches do not allow to have analytical descriptions of an optimal solution's theoretical properties as they are based on the numerical optimization of complex models.…”