Optimal building climate control: a solution based on nested dynamic programming and randomized optimization

We consider the problem of minimizing the electric energy consumption in the climate control of a building. More specifically, we suppose that the reference temperature in the building can be modulated to some extent during the day, so as to reduce the power request while limiting the introduced level of discomfort. To account for the uncertain building occupancy, we formulate the optimal energy management problem as a chance constrained optimization problem where one seeks for a state feedback policy that is robust over all occupancy realizations except for a set of predefined (small) probability. By exploiting the different time scales of the control and disturbance inputs, an algorithmic solution based on nested dynamic programming and randomized optimization is put forward and its parallel GPU implementation is discussed. A numerical example shows the efficacy of the approach.