  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.
