  In this paper, we address energy management for heating, ventilation, and
air-conditioning (HVAC) systems in buildings, and present a novel combined
optimization and control approach. We first formulate a thermal dynamics and an
associated optimization problem. An optimization dynamics is then designed
based on a standard primal-dual algorithm, and its strict passivity is proved.
We then design a local controller and prove that the physical dynamics with the
controller is ensured to be passivity-short. Based on these passivity results,
we interconnect the optimization and physical dynamics, and prove convergence
of the room temperatures to the optimal ones defined for unmeasurable
disturbances. Finally, we demonstrate the present algorithms through
simulation.
