International audienceIn France, buildings account for a significant portion of the electricity consumption (around 68%), due to an important use of electrical heating systems. This results in high peak load in winter and causes tensions on the production-consumption balance. In view of reducing such fluctuations, advanced control systems (including the Model Predictive Control framework) have been developed to shift heating load while maintaining indoor comfort and taking advantage of the building thermal mass. In this paper, a framework for developing optimisation-based control strategies to shift the heating load in buildings is introduced. The balanced truncation method and a time-continuous optimisation method were used to develop a re...