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Optimal control of irrigation: a dual modeling approach combining a mathematical and a simulation model; Application to Optirrig

I'm a PhD student at Inrae in Montpellier, more specifically at the UMR Mistea, working on optimizing the use of water resources in agriculture. My training covers the whole spectrum of mathematics, from theory to application, with a particular affinity for analysis and modeling. I want to work in the research world, and doing a thesis is the natural gateway to this.
In a context where the demand for water for agriculture continues to increase, and water resources are limited (or even in danger of diminishing), the question of how to manage its use arises, particularly in crop irrigation. The general idea of my subject is to look for ways of using water, i.e. at what time of the season and with what quantity crops will be irrigated, in order to optimize a certain objective (yield, financial...). To do this, we aim to describe, according to the assumptions chosen for the crop model, real-time irrigation strategies that take into account seasonal constraints and adapt to unknown medium- and long-term weather conditions. The ultimate aim is to contribute to the improvement of the Optirrig numerical model, by calibrating and implementing the optimal strategies obtained.
This subject mobilizes theoretical mathematical skills and tools (optimal control) in the service of a practical application (the use of water in agronomy). This interdisciplinarity brings together work and methods from different fields, and enables me to combine my appreciation of mathematics with a desire to tackle issues with a concrete relevance.

• Starting date : 1st October 2022
• Research unit: UMR Mistea, Inrae
• University : Université de Montpellier
• PhD school : I2S
• Scientific topic : Mathématiques et Modélisation
• Thesis management : Alain Rappaport, UMR Mistea, Inrae, Bruno Cheviron, UMR Mistea, Inrae 
• Thesis supervisors: Alain Rappaport, UMR Mistea, Inrae, Bruno Cheviron, UMR Mistea, Inrae, Sébastien Roux, UMR Mistea, Inrae 
• Funding: LabEx Numev - Inrae
• #DigitAg: Axe 6 : Modélisation et simulation (systèmes de production agricole), Axe 2 : Innovations en agriculture numérique, Challenge 6: La gestion des territoires agricoles, Challenge 5 : Les services de conseil agricole

Keywords: Optimal control, Irrigation, Dual modeling, Optirrig model

Abstract: This project concerns irrigation decision support tools 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 is to provide a decision i) in real time, based on the information provided by the sensors (in particular humidity) as feedback controls, ii) integrating seasonal management constraints such as quotas, iii) integrating meteorological information not precisely known in the medium and long term (“adaptative” control laws). The targeted approach is a "double modeling" approach that relies on developing a mathematical model that is a companion to the numerical model to be optimized, as well as on developing mathematical optimization methods on the companion model. These targeted methods are related to the optimal control theory for which promising first results have been obtained in previous works. The Phd advisors are research scientists in applied mathematics and the research scientist responsible for the development and operational uses of the numerical model Optirrig. A final goal of the project could be to test in real conditions the irrigation strategies developed in the thesis, via the installation of Optirrig on a Raspberry-Pi processor usabale to collect observation data of the water status of the soil and allowing a closed-loop control of irrigation.