Synthesis of Optimal Control Under State Constraints for Crop Fertigation

Mahugnon Gildas Dadjo (), Alain Rapaport (), Jérôme Harmand (), Rosane Ushirobira () and Denis Efimov ()
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Mahugnon Gildas Dadjo: Univ. Montpellier, INRAE, Institut Agro
Alain Rapaport: Univ. Montpellier, INRAE, Institut Agro
Jérôme Harmand: INRAE, Univ. Montpellier
Rosane Ushirobira: Univ. Lille, CNRS, UMR 9189 - CRIStAL
Denis Efimov: Univ. Lille, CNRS, UMR 9189 - CRIStAL

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 2, 27 pages

Abstract: Abstract We consider a generic model of fertigation for which the control variable is the irrigation flow rate. We first characterize conditions for which the dynamical system is viable by allowing maximal biomass production at harvesting time. Then, we consider the problem of minimizing the quantity of water delivered during a season under the viability constraint. We provide a complete optimal feedback synthesis as concatenations of bang and boundary arcs. We show that the optimal strategies can be radically different depending on the initial condition, leading to distinct ways to avoid water and nitrogen stresses for crops. Moreover, we characterize the possibility of having an infinity of optimal singular trajectories.

Keywords: Crop modeling; Water irrigation; State constraints; Viability theory; Optimal control; Boundary arcs; Singular arcs; 34H05; 93C15; 49J30; 92B05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02754-w

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