Multi-zone building control with thermal comfort constraints under disjunctive uncertainty using data-driven robust model predictive control

This paper proposes a novel data-driven robust model predictive control (MPC) framework for a multi-zone building considering thermal comfort and uncertain weather forecast errors. The control objective is to maintain each zone's temperature and relative humidity within the specified ranges by minimizing the energy usage of the underlying heating system. A state-space model is developed to use a hybrid physics-based and data-driven method for the multi-zone building's temperature and relative humidity. The temperature and humidity RMSEs between the state-space model and the EnergyPlus-based model are less than 0.25 °C and 5.9%, respectively. The uncertainty space is based on historical weather forecast error data, which are clustered by using a k-means clustering algorithm. Machine learning approaches, including 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. A robust MPC framework is built upon the proposed state-space model and data-driven disjunctive uncertainty set. 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 MPC are 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 framework can reduce up to 8.8% of total energy consumption compared to conventional robust MPC approaches. Moreover, the proposed framework can essentially satisfy the thermal constraints that certainty equivalent MPC and robust MPC largely violate.