  We consider robust output regulation of a partial differential equation model
describing temperature evolution in a room. More precisely, we examine a
two-dimensional room model with the velocity field and temperature evolution
governed by the incompressible steady state Navier-Stokes and
advection-diffusion equations, respectively, which coupled together form a
simplification of the Boussinesq equations. We assume that the control and
observation operators of our system are distributed, whereas the disturbance
acts on a part of the boundary of the system. We solve the robust output
regulation problem using a finite-dimensional low-order controller, which is
constructed using model reduction on a finite element approximation of the
model. Through numerical simulations, we compare performance of the
reduced-order controller to that of the controller without model reduction as
well as to performance of a low-gain robust controller.
