An optimal control methodology for plant growth--Case study of a water supply problem of sunflower

Lin Wu; François-Xavier Le Dimet; Philippe De Reffye; Bao-Gang Hu; Paul-Henry Cournède; Meng-Zhen Kang

hal-00705066, version 1

An optimal control methodology for plant growth--Case study of a water supply problem of sunflower

Lin Wu () ^1, 2, François-Xavier Le Dimet^a^, 3, Philippe De Reffye () ^4, 5, Bao-Gang Hu^b^, 6, Paul-Henry Cournède () ^4, 7, Meng-Zhen Kang () ⁶

Mathematics and Computers in Simulation 82, 5 (2012) 909-923

Résumé : An optimal control methodology is proposed for plant growth. This methodology is demonstrated by solving a water supply problem for optimal sunflower fruit filling. The functional-structural sunflower growth is described by a dynamical system given soil water conditions. Numerical solutions are obtained through an iterative optimization procedure, in which the gradients of the objective function, i.e. the sunflower fruit weight, are calculated efficiently either with adjoint modeling or by differentiation algorithms. Further improvements in sunflower yield have been found compared to those obtained using genetic algorithms in our previous studies. The optimal water supplies adapt to the fruit filling. For instance, during the mid-season growth, the supply frequency condenses and the supply amplitude peaks. By contrast, much less supplies are needed during the early and ending growth stages. The supply frequency is a determining factor, whereas the sunflower growth is less sensitive to the time and amount of one specific irrigation. These optimization results agree with common qualitative agronomic practices. Moreover they provide more precise quantitative control for sunflower growth.

a – Université Joseph Fourier - Grenoble I
b – Chinese Academy of Science
1 : Centre d'Enseignement et de Recherche en Environnement Atmosphérique (CEREA)
EDF – Ecole des Ponts ParisTech
2 : CLIME (INRIA Rocquencourt)
INRIA – Ecole des Ponts ParisTech
3 : MOISE (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
CNRS : UMR5224 – INRIA – Laboratoire Jean Kuntzmann – Université Joseph Fourier - Grenoble I – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
4 : DIGIPLANTE (INRIA Saclay - Ile de France)
INRIA – Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR – Ecole Centrale Paris
5 : BotAnique et BioinforMatique de l'Architecture des Plantes (AMAP)
Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR51 – CNRS : UMR5120 – Institut de recherche pour le développement [IRD] – Institut national de la recherche agronomique (INRA) : UR0931 – Université Montpellier II - Sciences et techniques
6 : Eco-informatics (LIAMA)
Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] – CNRS – Institut national de la recherche agronomique (INRA) – INRIA – Chinese Academy of Science (CAS) – Institute of Automation, Chinese Academy of Sciences
7 : Mathématiques Appliquées aux Systèmes - EA 4037 (MAS)
Ecole Centrale Paris

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Contributeur : Nathalie Gaudechoux <>
Soumis le : Mercredi 6 Juin 2012, 17:12:28
Dernière modification le : Jeudi 7 Juin 2012, 15:55:05

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DOI : 10.1016/j.matcom.2011.12.007

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%% hal-00705066, version 1
%% http://hal.inria.fr/hal-00705066
@article{wu:hal-00705066,
    hal_id = {hal-00705066},
    url = {http://hal.inria.fr/hal-00705066},
    title = {{An optimal control methodology for plant growth--Case study of a water supply problem of sunflower}},
    author = {Wu, Lin and Le Dimet, Fran{\c c}ois-Xavier and De Reffye, Philippe and Hu, Bao-Gang and Courn{\`e}de, Paul-Henry and Kang, Meng-Zhen},
    abstract = {{An optimal control methodology is proposed for plant growth. This methodology is demonstrated by solving a water supply problem for optimal sunflower fruit filling. The functional-structural sunflower growth is described by a dynamical system given soil water conditions. Numerical solutions are obtained through an iterative optimization procedure, in which the gradients of the objective function, i.e. the sunflower fruit weight, are calculated efficiently either with adjoint modeling or by differentiation algorithms. Further improvements in sunflower yield have been found compared to those obtained using genetic algorithms in our previous studies. The optimal water supplies adapt to the fruit filling. For instance, during the mid-season growth, the supply frequency condenses and the supply amplitude peaks. By contrast, much less supplies are needed during the early and ending growth stages. The supply frequency is a determining factor, whereas the sunflower growth is less sensitive to the time and amount of one specific irrigation. These optimization results agree with common qualitative agronomic practices. Moreover they provide more precise quantitative control for sunflower growth.}},
    language = {Anglais},
    affiliation = {Centre d'Enseignement et de Recherche en Environnement Atmosph{\'e}rique - CEREA , CLIME - INRIA Rocquencourt , MOISE - INRIA Grenoble Rh{\^o}ne-Alpes / LJK Laboratoire Jean Kuntzmann , DIGIPLANTE - INRIA Saclay - Ile de France , BotAnique et BioinforMatique de l'Architecture des Plantes - AMAP , Eco-informatics - LIAMA , Math{\'e}matiques Appliqu{\'e}es aux Syst{\`e}mes - EA 4037 - MAS},
    publisher = {Elsevier},
    pages = {909-923},
    journal = {Mathematics and Computers in Simulation},
    volume = {82},
    number = {5 },
    audience = {internationale },
    doi = {10.1016/j.matcom.2011.12.007 },
    year = {2012},
    month = Jan,
}

%F hal-00705066, version 1
%0 Journal Article
%U http://hal.inria.fr/hal-00705066
%2 INFO:INFO_MO
%T An optimal control methodology for plant growth--Case study of a water supply problem of sunflower
%A Wu, Lin
%A Le Dimet, François-Xavier
%A De Reffye, Philippe
%A Hu, Bao-Gang
%A Cournède, Paul-Henry
%A Kang, Meng-Zhen
%+ Centre d'Enseignement et de Recherche en Environnement Atmosphérique - CEREA , CLIME - INRIA Rocquencourt , MOISE - INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann , DIGIPLANTE - INRIA Saclay - Ile de France , BotAnique et BioinforMatique de l'Architecture des Plantes - AMAP , Eco-informatics - LIAMA , Mathématiques Appliquées aux Systèmes - EA 4037 - MAS
%X An optimal control methodology is proposed for plant growth. This methodology is demonstrated by solving a water supply problem for optimal sunflower fruit filling. The functional-structural sunflower growth is described by a dynamical system given soil water conditions. Numerical solutions are obtained through an iterative optimization procedure, in which the gradients of the objective function, i.e. the sunflower fruit weight, are calculated efficiently either with adjoint modeling or by differentiation algorithms. Further improvements in sunflower yield have been found compared to those obtained using genetic algorithms in our previous studies. The optimal water supplies adapt to the fruit filling. For instance, during the mid-season growth, the supply frequency condenses and the supply amplitude peaks. By contrast, much less supplies are needed during the early and ending growth stages. The supply frequency is a determining factor, whereas the sunflower growth is less sensitive to the time and amount of one specific irrigation. These optimization results agree with common qualitative agronomic practices. Moreover they provide more precise quantitative control for sunflower growth.
%G Anglais
%J Mathematics and Computers in Simulation
%8 2012-01-00
%2 internationale
%I Elsevier
%V 82
%N 5
%P 909-923
%R 10.1016/j.matcom.2011.12.007

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