  Efficiency, comfort, and convenience are three major aspects in the design of
control systems for residential Heating, Ventilation, and Air Conditioning
(HVAC) units. In this paper we propose an optimization-based algorithm for HVAC
control that minimizes energy consumption while maintaining a desired
temperature in a room. Our algorithm uses a Computer Fluid Dynamics model,
mathematically formulated using Partial Differential Equations (PDEs), to
describe the interactions between temperature, pressure, and air flow. Our
model allows us to naturally formulate problems such as controlling the
temperature of a small region of interest within a room, or to control the
speed of the air flow at the vents, which are hard to describe using
finite-dimensional Ordinary Partial Differential (ODE) models. Our results show
that our algorithm produces significant energy savings without a decrease in
comfort.
