Optimal Control for Indoor Vertical Farms Based on Crop Growth

Abstract

Vertical farming allows for year-round cultivation of a variety of crops, overcoming environmental limitations and ensuring food security. This closed and highly controlled system allows the plants to grow in optimal conditions, so that it reaches maturity faster and yields more than on a conventional outdoor farm. However, one of the challenges of vertical farming is the high energy consumption. In this work, we optimize wheat growth using an optimal control approach with two objectives: first, we optimize inputs such as water, radiation, and temperature for each day of the growth cycle and second, we optimize the duration of the plant's growth period to achieve the highest possible yield over a whole year. For this, we use a nonlinear, discrete-time hybrid model based on a simple universal crop model that we adapt to make the optimization more efficient. Using our approach, we find an optimal trade-off between used resources, net profit of the yield, and duration of a cropping period, thus increasing the annual yield of crops significantly while keeping input costs as low as possible. This work demonstrates the high potential of control theory in the discipline of vertical farming.