Robust MPC for Building Energy Optimization With Continuous and Discrete Inputs

We propose a computationally efficient model predictive control (MPC) approach for optimal electrical and thermal energy flows in non‐residential buildings, where components such as heat pumps and heating rods introduce discrete variables, necessitating the solution of mixed integer quadratic programming (MIQP) problems. To reduce the computational effort of solving these problems, we relax the discrete dynamics along the horizon and incorporate the resulting error as a bounded additive disturbance. This compensates for suboptimality and potential constraint violations of the relaxed approach in closed‐loop operation. We employ multi‐stage MPC as a robust MPC framework to handle these disturbances. The recursive feasibility of the proposed multi‐stage MPC formulation is established using a robust control invariant terminal set. We evaluate the performance of the proposed multi‐stage MPC in simulations for a real office building. The results demonstrate that the proposed computationally efficient robust formulation achieves performance comparable to the optimal solution obtained by solving the MIQP problems for the entire horizon while ensuring constraint satisfaction in closed‐loop simulations.