This paper describes the methodology to apply discrete-time optimal control to a building and its HVAC installation, Simulation -based results concerning a passive solar commercial building are presented and discussed .The simulation environment includes the RTNSYS TYPE 56 as reference building model and HVAC detailed models to test the controller with realistic control signals . The optimal controller's sensitivity to meteorological forecasting quality and to other factors is analysed. Its performance is compared to results obtained with a conventional control system to assess the relevancy of optimal control for this application.