## Section: Application Domains

### Optimal control for plants

Participant : L. Wu (GreenLab associated team).

The ultimate goal of mathematical models is to optimize different situations under various constraints. A good example for plants models is the water supply in stress conditions. How to provide the optimal quantity of water at each growth cycle in order to optimize the yield? The amount of water in the soil depends of the water supply and of the plant transpiration that drive the plant photosynthesis. The Phd of Wu Lin from GrennLab associated team working in Idopt Inria project, as solved this problem, using the optimal control method. The soil water balance model chosen was the FSTW, acting with the theoretical plant transpiration given by the GreenLab model.

Results show that both the shape of the distribution of the water supply per growth cycle and the period of the supply are important. Compare to the control uniform distribution it was found by computation that a 5 days period for irrigation under an optimized water distribution improve the yield of more than 30 %. This result is a first step towards virtual agronomical experiments. The same kind of applications could be undertaken on fertilizers, or to prevent excessive pollution from the use of insecticides or herbicides.