Control of the crop-production in a network of agricultural plots

In the present paper, we propose a strategy to control the crop-production of a network of agricultural plots. The network is composed of rangeland and cropland subsystems that are connected to each other through the livestock that is a vector of nutrient from rangeland to cropland. The objective is to reach a given crop production (at the scale of the whole network) while ensuring a minimal production in each of the cropland plot. To take into account the saturation constraints on the control inputs (that are the rangeland removal rates and the manure distribution coefficients), we use a method based on a time-scale transformation. After designing the control law, we apply it on a simple numerical example to highlight the results.