We deal with the problem of energy management in buildings subject to
uncertain occupancy. To this end, we formulate this as a finite horizon
optimization program and optimize with respect to the windows' blinds position,
radiator and cooling flux. Aiming at a schedule which is robust with respect to
uncertain occupancy levels while avoiding imposing arbitrary assumptions on the
underlying probability distribution of the uncertainty, we follow a data driven
paradigm. In particular, we apply an incremental scenario approach methodology
that has been recently proposed in the literature to our energy management
formulation. To demonstrate the efficacy of the proposed implementation we
provide a detailed numerical analysis on a stylized building and compare it
with respect to a deterministic design and the standard scenario approach
typically encountered in the literature. We show that our schedule is not
agnostic with respect to uncertainty as deterministic approaches, while it
requires fewer scenarios with respect to the standard scenario approach, thus
resulting in a less conservative performance
