This paper tackles the design of a reference governor strategy based on model predictive control (MPC) which allows to improve economics of conventional relay-based thermostats in residential buildings. In this set up, MPC serves as a supervisory controller which generates optimal setpoints for the thermostat. The thermostat, which operates in an on/off manner, then controls the heating actuator that influences the indoor temperature. We show how to include the dynamical behavior of such a thermostat into the MPC optimization problem. Optimal setpoints can then be obtained by solving a mixed integer linear programming problem. Efficiency of the proposed strategy is verified on a simulation case study.
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