A robust data-driven MPC for greenhouse temperature control

This paper addresses the problem of robust temperature control in greenhouses, where maintaining optimal thermal conditions is essential for crop productivity, while accounting for uncertainties in solar irradiance and ambient temperature. We propose a novel spatially distributed model for greenhouse temperature dynamics, formulated through a finite difference scheme over a convex polyhedral sloped-roof geometry, incorporating volumetric heat sources from solar radiation and an inverter-based HVAC system. The HVAC action is represented by a linear-in-input kernel with directional weighting, ensuring convexity with respect to the control action, while boundary heat exchange is treated via ghost-point Robin conditions. Uncertainties are handled through a scenario-based robust model predictive control formulation that preserves convexity and guarantees optimality. The resulting problem is solved using a forward-backward scheme that exploits the structured canonical form of the discretized dynamics. The approach is validated using data from a smart greenhouse in Genova, Italy, with out-of-sample tests confirming robustness.