cooling.

Let us now validate the model by comparing the zone temperature time response of the RC network to EnergyPlus results under simplified conditions. The goal is not to exactly match EnergyPlus, but rather to show that the dominant response is plausibly close. To do this, we have simulated the building using first the RC network and then EnergyPlus under the following set of conditions:

-   a step change in air, ground, and sky infrared temperatures from 10$^{\circ}\textrm{C}$ to 20$^{\circ}\textrm{C}$,

-   no wind or humidity, and

-   EnergyPlus heat transfer algorithms: `Simple` convection for interior, `SimpleCombined` for exterior, and `CTF` (conduction transfer function) for walls.

The RC network implementation lacks support for sky infrared transfer through windows; by matching the sky radiant temperature to the outside air temperature, we have removed this source of discrepancy from the simulation. Under the simplified conditions, very similar response times (Figure \[fig:rcVersusEp\]) suggest that the RC model is adequate for demonstration.

![\[fig:rcVersusEp\]RC network (solid) and EnergyPlus (dashed) simulation results for a step change in ambient temperature.](comparisonEplusToRC)

 {#section .unnumbered}

\[sec:Stochastic-occupancy-model\]Stochastic Occupancy Model
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The heart of our method is its on-line trained Markov occupancy model that quickly adapts and enables the MPC to predict occupancy. 