Optimal Control of a Bioeconomic Crop-Energy System with Energy Reinvestment
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909900225904640 |
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| author | Dekkaki, Othman Cherkaoui |
| author_facet | Dekkaki, Othman Cherkaoui |
| contents | We develop an optimal control model for allocating agricultural crop residues between bioenergy production and soil fertility restoration. The system captures a novel circular feedback: a fraction of cumulative energy output is reinvested into soil productivity, linking energy use with ecological regeneration. The dynamics are governed by a nonlinear three-state system describing soil fertility, residue biomass, and accumulated energy, with a single control representing the proportion of biomass diverted to energy. The objective is to maximize a discounted net benefit that accounts for energy revenue, soil value, and operational costs. We apply the Pontryagin Maximum Principle in current-value form to derive necessary optimality conditions and characterize the structure of optimal controls. Numerical simulations based on direct optimization reveal interior and switching regimes, and show how planning horizon and reinvestment efficiency influence optimal strategies. The results highlight the strategic role of energy reinvestment in achieving sustainable residue management. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_11381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Control of a Bioeconomic Crop-Energy System with Energy Reinvestment Dekkaki, Othman Cherkaoui Optimization and Control Dynamical Systems We develop an optimal control model for allocating agricultural crop residues between bioenergy production and soil fertility restoration. The system captures a novel circular feedback: a fraction of cumulative energy output is reinvested into soil productivity, linking energy use with ecological regeneration. The dynamics are governed by a nonlinear three-state system describing soil fertility, residue biomass, and accumulated energy, with a single control representing the proportion of biomass diverted to energy. The objective is to maximize a discounted net benefit that accounts for energy revenue, soil value, and operational costs. We apply the Pontryagin Maximum Principle in current-value form to derive necessary optimality conditions and characterize the structure of optimal controls. Numerical simulations based on direct optimization reveal interior and switching regimes, and show how planning horizon and reinvestment efficiency influence optimal strategies. The results highlight the strategic role of energy reinvestment in achieving sustainable residue management. |
| title | Optimal Control of a Bioeconomic Crop-Energy System with Energy Reinvestment |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2510.11381 |