Optimal Control of Autonomous Greenhouses

Abstract

The world population is growing rapidly and the demand for healthy food grows with it. Greenhouse cultivation provides an efficient way to grow crops in a protected and controlled environment. In the past, many greenhouse control algorithms have been developed. How- ever, the majority of these algorithms rely on an explicit parametric model description of the greenhouse. These models are often based on physical laws such as conservation of mass and energy and contain many parameters which should be identified. Due to the complex and highly non-linear dynamics of greenhouses, these models might not be applicable to control greenhouses other than the one for which the model has been designed and identified. Hence, in current horticultural practice these control algorithms are scarcely used. Therefore, the need rises for a control algorithm which does not rely on a parametric system representa- tion but rather on input/output data of the greenhouse system, hereby establishing a way to control the system with unknown or unmodeled dynamics. A recently proposed algo- rithm, Data-Enabled Predictive Control (DeePC), is able to replace system identification, state estimation and future trajectory prediction by one single optimization framework. The algorithm exploits a non-parametric model constructed solely from input/output data of the system. This algorithm is employed in order to control the greenhouse climate. It is shown that in numerical simulation the DeePC algorithm is able to control the greenhouse climate. A comparison is made with the conventional Nonlinear Model Predictive Control (NMPC) algorithm in order to show the differences between a predictive control algorithm that has direct access to the non-linear greenhouse simulation model and a purely data-driven predic- tive control algorithm. Both algorithms are compared based on reference tracking accuracy and computational time. Furthermore, it is shown in numerical simulation that the DeePC algorithm is able to cope with changing dynamics within the greenhouse system throughout the crop cycle.