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

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.

کلیدواژه ها:

optimal control ، Bioeconomic modeling ، Agricultural residue management ، Energy-soil feedback ، Pontryagin Maximum Principle