Multi-Scenario Model Predictive Control for Greenhouse Crop Production Considering Market Price Uncertainty

Abstract

This paper presents a stochastic model predictive control (SMPC) strategy to maximize the economic profit of a greenhouse crop production. The strategy consists of an optimization problem that is solved with a multi-scenario MPC formulation (MS-MPC). It considers the uncertainty of market price by using its historical evolution per year as multiple price scenarios in the cost function. MS-MPC calculates a single set of dates to harvest and sell the crop production that optimizes profits for all the considered scenarios. In addition, MS-MPC determines the optimal temperature references that should be achieved inside the greenhouse for the growth of the crop. A case study for a Mediterranean tomato crop is simulated to analyze the performance of the developed MS-MPC strategy using a hierarchical control architecture with two layers. In the upper layer, MS-MPC calculations are executed following a receding horizon implementation. In the lower layer, regulatory control techniques are applied to reach the optimal temperature references by using natural ventilation and a heating system. Results show that MS-MPC can improve economic profits compared to the use of an average price scenario for the MPC calculations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the need of greenhouse farmers for strategies that maximize profit considering market prices and crop production dynamics. It is not easy for them to make decisions to achieve such long-term objectives while minimizing economic risks, because market prices are very difficult to predict. As a solution, this work presents a novel control strategy to maximize profits by means of automatic selection of the best possible dates to harvest and sell the crop production. This selection is made thanks to considering the uncertainty of market prices in the control strategy by evaluating different scenarios, which are recorded evolutions of the prices from previous years. Although the strategy was tested in simulation, results suggest that using multiple scenarios of historical prices is better for the optimization of profits than just considering an average yearly trend of prices. The more scenarios are considered, the more protection against possible evolution of market prices is obtained. In future research, this control strategy could be extended to include other uncertainties of factors affecting decision making, such as weather forecasts.