Plant Performance in Precision Horticulture: Optimal climate control under stochastic uncertainty

Abstract

This paper presents a risk mitigating, time-varying feedback control algorithm for crop production when state dynamics are subject to uncertainty. The model based case study concerns a 40 day production round of lettuce in a greenhouse where control input consists of daily and nightly temperature set points. The control problem was formulated in terms of a stochastic Markov decision process with the objective to maximize the expected net revenue at harvest time. The importance of time-varying feedback and of risk mitigation was investigated by making a comparison with a controller that takes uncertainty into account but is static and a controller which is dynamic but ignores the uncertainty in the state dynamics. For the case of heat limited crop growth, and strict requirements on harvest weight precision, the dynamic stochastic controller outperformed the static controller in terms of both maximal expected net revenue (by 19 %) and state precision at harvest time (with 50 % less standard deviation). It also outperformed the deterministic controller for both criteria (15 % in maximal expected net revenue and 8 % less standard deviation). A detailed sensitivity analysis showed that such improvements in performance levels are robust, since they hold over large ranges of uncertainty in state dynamics, required harvest precision levels, starting days, and initial weights. The results provide insights in potential of dynamic feedback and risk mitigation strategies for high precision requirements under uncertainty. Although the results should be interpreted with caution, they illustrate the considerable potential benefit for stochastic greenhouse climate control under uncertainty when high precision is required.