Modelling the greenhouse lettuce crop by means of the daily interaction of two independent models

One of the most important works for optimizing the dry matter production in greenhouses is the one done by van Henten. A difficulty for synthesizing the optimal control scheme, proposed by van Henten, it is due to the high non-linearities presented in the van Henten´s model. Because of these high non-linearities, the control law synthesis procedure is a challenging task indeed. In particular, the optimal control law proposed for this model can not be expressed in an explicit way, and it is necessary to solve a nonlinear programming algorithm in each sampling period. In order to tackle this difficulty, in this paper we propose a simplification of the van Henten´s model. This simplification is done in two steps: firstly we separate the van Henten´s model into two independent models: one for the day period and the other one to the night period. Then, we express explicitly the relative growth rate in terms of the environmental variables.