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<p>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.</p>

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Synthesis of Optimal Control Under State Constraints for Crop Fertigation

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Mahugnon Gildas Dadjo,
  • Alain Rapaport,
  • Jérôme Harmand,
  • Rosane Ushirobira,
  • Denis Efimov

摘要

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.