could be extended to work on-line, ongoing maintenance remains a source of long-term cost neglected by the literature. An occupancy model invariably becomes out-of-date unless it is periodically retrained or can incrementally refine itself with new observations. Our work uses on-line Bayesian inference for stable performance without ongoing manual effort.

![image](architecture)

The paper progresses as follows. First, we outline the problem formulation. Second, we describe the stochastic occupancy model and its on-line training algorithm. Third, we discuss its integration with model predictive control. Finally, we present simulation results using real-world occupancy data and compare our method’s performance to a correctly set scheduled controller and to an occupancy-triggered controller. Throughout the discussion, the control scenario is kept deliberately simple to emphasize the contribution of occupancy learning and its use with MPC.[^1]

\[sec:Problem-Statement\]Problem Statement
==========================================

We wish to minimize the total energy usage of a building heating (or cooling) system while maintaining occupant comfort. Versus conventional occupancy-triggered or scheduled control, we aim to

-   boost comfort by conditioning the space before occupants arrive,

-   limit energy consumption by not running the system too early, and

-   exploit stored thermal energy by reducing power before occupants leave.

Our approach is based on MPC 