A Non-Linear Optimal Greenhouse Control Problem Solved by Linear Programming

The purpose of the study is the development of Model Predictive Control for greenhouse operation, which means that a new optimal control problem is solved each time the weather prediction is updated. A simplified non-linear dynamic model of greenhouse crop growth with constraints on the state and the control signal is given. The weather is assumed to be known. The optimization criterion is to minimize the heating cost. The resulting optimal control problem is analysed from the point of view of the Pontryagin maximum principle. It is shown that this particular problem can be solved numerically by linear programming, and that it can also be formulated as a network flow problem. The solution is presented and it is found that, in cold weather, it is worthwhile to deviate from the "blueprint" and instead heat during the night when the thermal screens are in place and the heat loss small, while keeping the minimally allowed temperature during daytime. Assuming a perfect weather forecast, heating costs in the analysed case are lowered by 22%, relative to a "blueprint" operation of keeping the temperature constant.