1. Optimal control of a crop irrigation model under water scarcity
- Author
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Carole Sinfort, Kenza Boumaza, Nesrine Kalboussi, Alain Rapaport, Sebastien Roux, Rapaport, Alain, Institut Convergences en Agriculture Numérique - - DIGITAG2016 - ANR-16-CONV-0004 - CONV - VALID, Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université de Carthage - University of Carthage, Information – Technologies – Analyse Environnementale – Procédés Agricoles (UMR ITAP), Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), ANR-16-CONV-0004,DIGITAG,Institut Convergences en Agriculture Numérique(2016), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), laboratoire de traitement des eaux naturelles (LabTEN), Centre de Recherche et Technologies des Eaux (CERTE), AVERROES PhD Grant, Euro-mediterranean TREASURE network (Treatment and Sustainable Reuse of Effluents in semi-arid climates), and ANR-18-IC4W-0002,Control4Reuse,Technologies de contrôle de processus pour les géants de l'eau(2018)
- Subjects
0209 industrial biotechnology ,Irrigation ,Control and Optimization ,media_common.quotation_subject ,0208 environmental biotechnology ,[SDV.SA.AGRO]Life Sciences [q-bio]/Agricultural sciences/Agronomy ,Context (language use) ,02 engineering and technology ,Agricultural engineering ,Dynamical system ,Scarcity ,optimal control ,020901 industrial engineering & automation ,Control theory ,water management ,Production (economics) ,feedback synthesis ,Mathematics ,media_common ,[SDV.SA.AGRO] Life Sciences [q-bio]/Agricultural sciences/Agronomy ,singular arcs ,Applied Mathematics ,Irrigation scheduling ,[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC] ,Optimal control ,020801 environmental engineering ,Control and Systems Engineering ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Software ,crop irrigation - Abstract
International audience; We consider a simple crop irrigation model and study the optimal control which consists of maximizing the biomass production at harvesting time. A specificity of this work is to impose a quota on the water used for irrigation, in a context of limited resources. The model is written as a 2d non-autonomous dynamical system with a state constraint, and a non-smooth right member given by threshold-based soil and crop water stress functions. We show that when the water quota is below the threshold giving the largest possible production, the optimal strategy consists of irrigating once. We then show that the optimal solution can have one or several singular arcs, and therefore be better than simple bang-bang controls, as commonly used. The gains over the best bang-bang controls are illustrated on numerical simulations. These new feedback controls that we obtain are a promising first step towards the concrete application of control theory to the problem of optimal irrigation scheduling under water scarcity.
- Published
- 2020
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