Hybrid Physics-based and Data-driven Model Predictive Control for Multi-Zone Building’s Thermal Comfort Under Disjunctive Uncertainty

This paper proposes a hybrid approach that utilizes the knowledge of the disjunctive uncertainty sets and incorporates them into the model predictive control (MPC). This approach targets multi-zone building control to the thermal comfort, and it’s robust to the uncertain weather forecast errors. The control objective is to maintain each zone’s temperature and relative humidity within the specified ranges by leveraging the minimum cost of energy of the underlying heating system. The hybrid model is constructed by using a physics-based and regression method for the temperature and relative humidity of each zone in the building. The uncertainty space is on the basis of historical weather forecast error data, which are captured by a group of disjunctive uncertainty sets using a k-means clustering algorithm. Machine learning approaches based on principal component analysis and kernel density estimation are used to construct each basic uncertainty set and reduce the conservatism of resulting robust control action under disturbances. Based on the proposed hybrid model and data-driven disjunctive uncertainty set, a robust MPC framework is further developed. An affine disturbance feedback rule is employed to obtain a tractable approximation of the robust MPC problem. Besides, the feasibility and stability of the proposed hybrid approach are ensured and discussed in detail. A case study of controlling temperature and relative humidity of a multi-zone building in Ithaca, New York, USA, is presented. The results demonstrate that the proposed hybrid approach can reduce 9.8% to 17.9% of total energy consumption compared to conventional robust MPC approaches. Moreover, the proposed hybrid approach can essentially satisfy the thermal constraints that certainty equivalent MPC and robust MPC largely violate.