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In this paper, we design real-time decentralized and distributed controlschemes for Heating Ventilation and Air Conditioning (HVAC) systems in energyefficient buildings. The control schemes balance user comfort and energysaving, and are implemented without measuring or predicting exogenousdisturbances. Firstly, we introduce a thermal dynamic model of building systemsand formulate a steady-state resource allocation problem, which aims tominimize the aggregate deviation between zone temperatures and their setpoints, as well as the building energy consumption, subject to practicaloperating constraints, by adjusting zone flow rates. Because this problem isnonconvex, we propose two methods to (approximately) solve it and to design thereal-time control. In the first method, we present a convex relaxation approachto solve an approximate version of the steady-state optimization problem, wherethe heat transfer between neighboring zones is ignored. We prove the tightnessof the relaxation and develop a real-time decentralized algorithm to regulatethe zone flow rate. In the second method, we introduce a mild assumption underwhich the original optimization problem becomes convex, and then a real-timedistributed algorithm is developed to regulate the zone flow rate. In bothcases, the thermal dynamics can be driven to equilibria which are optimalsolutions to those associated steady-state optimization problems. Finally,numerical examples are provided to illustrate the effectiveness of the designedcontrol schemes.

Decentralized and Distributed Temperature Control via HVAC Systems in Energy Efficient Buildings