Low nitrate lettuce cultivations in greenhouses - Optimal control in the presence of measurable disturbances

This thesis is about optimal greenhouse lettuce cultivations such that lettuce nitrate accumulation above EU imposed maximum concentrations is prevented at maximum profits. This case is an example of two general classes of problems: firstly, crop quality improvement through adjustment of environmental conditions during cultivation and secondly, optimal control of processes that are carried out with a significant number of limitations on process variables while being affected by disturbances. Finding solutions for this problem will be interesting for people working in the area of horticulture as well as for people working in the area of optimal control.  This problem can be solved mathematically through the computation of optimal trajectories of greenhouse climate variables and their affecting controls. The variables of interest are greenhouse air temperature, relative humidity ratio and greenhouse air CO ₂ -concentration while the control inputs are heating pipe temperatures, CO ₂ -enrichment flow rates and ventilation rates.A so-called closed-loop suboptimal control algorithm is presented eventually. To build this algorithm, equations, cost functions, constraints and disturbances are presented first. Then results of open loop optimisations with perfect a-priori knowledge of disturbances are presented. These results are analysed for characteristic patterns. These patterns and necessary optimality conditions are applied to obtain operational modes for the design of the algorithm. Symbolic computations are also employed here. The modes can be evaluated very efficiently, which makes the algorithm highly efficient computationally.