Chance constrained stochastic MPC for building climate control under combined parametric and additive uncertainty

This paper presents a chance constrained stochastic model predictive control (SMPC) approach for building climate control under combined parametric and additive uncertainties. The proposed SMPCap approach enables the quantification, and manipulation, of both the mean and covariance of the stochastic system states and inputs. Its enhanced uncertainty anticipation is shown to induce improved thermal comfort in closed-loop simulations compared to the conventional deterministic MPC (DMPC) and the state-of-the-art SMPCa only accounting for additive uncertainties, at the cost of a maximum relative increase in energy use of 21.6% and 4.2%, respectively. By incorporating the SMPCap strategy in an integrated optimal control and design (IOCD) approach, its additional added value for obtaining a more appropriate, yet robust, heat supply system sizing is illustrated. Via simulations, size reductions up to 33.3% are shown to be achievable for a terraced single-family dwelling without increasing thermal discomfort compared to an IOCD approach incorporating DMPC.