Optimal control of a bioeconomic crop-energy system with energy reinvestment

Document Type : Research Article

Author

College of Computing, University Mohammed VI Polytechnic, Benguerir, Morocco

Abstract

We develop a continuous-time optimal control model for allocating agricultural crop residues between bioenergy production and soil fertility restoration. The system includes a circular reinvestment channel: a portion of the accumulated bioenergy stock is reinvested to enhance soil fertility, thereby closing the loop between energy use and ecological regeneration. The dynamics are governed by a three-state system with a single allocation control. 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 a bang–interior–bang control; no singular arc under our parameterization. Direct optimization confirms a quasi-turnpike phase and shows how the planning horizon and reinvestment efficiency shift switching times and interior duration. The results highlight the strategic role of energy reinvestment in sustainable residue management.

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References

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Journal of Mathematical Modeling
Volume 14, Issue 1
March 2026
Pages 327-346

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