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

Cherkaoui Dekkaki, Othman

doi:10.22124/jmm.2025.31369.2815

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

Articles in Press

Document Type : Research Article

Author

Othman Cherkaoui Dekkaki

College of Computing, Mohammed IV Polytechnic University, Benguerir Morocco.

10.22124/jmm.2025.31369.2815

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.

Keywords