Optimal temperature setpoint control for a complete greenhouse crop cycle under growth uncertainty

This paper proposes to plan crop production over a complete growing season, by solving a control problem that optimises expected net revenue under stochastic disturbances. Production specifications with payouts only at harvest time (i.e. a reward only at harvest time) and under precise weight constraints on the harvested crop were considered. A case study was conducted for lettuce production in a greenhouse under Dutch weather conditions. Optimal control policies were calculated for weather measured on three different days, three different values for energy costs, and an uncertainty analysis was carried out under varying harvest weight requirements, state dynamics uncertainty levels, initial crop weight and starting time of the production round. The optimal controller balances daily energy costs and the expected maximum harvest revenues and uses state- and time-dependent feedback to adapt its actions under uncertainty. A control policy that is not based on uncertainty, is shown to perform substantially worse, with 15% less net revenues. A control policy without dynamic feedback even lead to a loss of 19% in net revenues. The sensitivity analysis showed that these performance differences persist over large ranges in uncertainty level, harvest weight constraints, deviations from the optimal starting day, and deviations in initial crop weight. Altogether, the results indicate that dynamic feedback, and uncertainty modelling can substantially improve economic outcomes in greenhouse climate control design.