This project concerns decision support tools in crop irrigation based on the optimization of numerical models developed at INRAE ​​within the AQUA department (Optirrig model) in a context of climate change and preservation of water resources.

The motivation of this optimization is to provide a decision:

• i) in real time,
• ii) integrating quota-type seasonal management constraints,
• iii) integrating meteorological information not known in the medium and long term.

The targeted approach is a "double modeling" which is based on the development and optimization of a mathematical model companion of the numerical model to be optimized, as well as on the implementation or extension of mathematical optimization methods on the companion model belonging to the field of optimal control theory and for which the first promising results have been obtained in the context of previous work.

The thesis will be co-directed by researchers in applied mathematics and the researcher responsible for the development and operational uses of the Optirrig numerical model.

Keywords: Pontryagin's maximum principle ; Constrained dynamical system ; Crop irrigation model ; Numerical simulations ; Climatic hazards.