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State Dependent Riccati for dynamic boundary control to optimize irrigation in Richards’ equation framework

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  • Alla, Alessandro
  • Berardi, Marco
  • Saluzzi, Luca

Abstract

We present an approach for the optimization of irrigation in a Richards’ equation framework. We introduce a proper cost functional, aimed at minimizing the amount of water provided by irrigation, at the same time maximizing the root water uptake, which is modeled by a sink term in the continuity equation. The control is acting on the boundary of the dynamics and due to the nature of the mathematical problem we use a State Dependent Riccati approach which provides suboptimal control in feedback form, applied to the system of ODEs resulting from the Richards’ equation semidiscretization in space. The problem is tested with existing hydraulic parameters, also considering proper root water uptake functions. The numerical simulations also consider the presence of noise in the model to further validate the use of a feedback control approach.

Suggested Citation

  • Alla, Alessandro & Berardi, Marco & Saluzzi, Luca, 2025. "State Dependent Riccati for dynamic boundary control to optimize irrigation in Richards’ equation framework," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 261-275.
    • Handle: RePEc:eee:matcom:v:232:y:2025:i:c:p:261-275
    DOI: 10.1016/j.matcom.2024.12.020
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    References listed on IDEAS

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    1. A. Khoutaibi & L. Maniar & D. Mugnolo & A. Rhandi, 2022. "Parabolic equations with dynamic boundary conditions and drift terms," Mathematische Nachrichten, Wiley Blackwell, vol. 295(6), pages 1211-1232, June.
    2. Sofia O. Lopes & Fernando A. C. C. Fontes & Rui M. S. Pereira & MdR de Pinho & A. Manuela Gonçalves, 2016. "Optimal Control Applied to an Irrigation Planning Problem," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, June.
    3. Falcone, Maurizio & Kirsten, Gerhard & Saluzzi, Luca, 2023. "Approximation of optimal control problems for the Navier-Stokes equation via multilinear HJB-POD," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    4. S. C. Beeler & H. T. Tran & H. T. Banks, 2000. "Feedback Control Methodologies for Nonlinear Systems," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 1-33, October.
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