Optimal control of non-smooth greenhouse models

Controlling a greenhouse climate aims at achieving good crop production objectives, while reducing expenses related to energy consumption. The use of methods based on optimal control theory generally fails to determine a long-term strategy, nor can it handle the gaps between the modeling of the system and its actual behavior. In keeping with preceding works on receding time horizon, we consider the problem of online determination of the optimal action, for a given state of the system, represented as a Markov decision process. In a greenhouse, if we make the assumptions that the sources of randomness (weather, observation noise) are independent of the user's actions, the stochastic problem can be solved numerically by computing deterministic optimal controls for different scenarios of external conditions. It is for this purpose that we have developed a heuristic method to solve efficiently deterministic optimal control problems, with a long-time horizon and a system discontinuous with respect to the control variables. This method is illustrated on a greenhouse-crop model based on GreenLab.