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

In this paper, we design real-time decentralized and distributed control schemes for Heating Ventilation and Air Conditioning (HVAC) systems in energy efficient buildings. The control schemes balance user comfort and energy saving, and are implemented without measuring or predicting exogenous disturbances. Firstly, we introduce a thermal dynamic model of building systems and formulate a steady-state resource allocation problem, which aims to minimize the aggregate deviation between zone temperatures and their set points, as well as the building energy consumption, subject to practical operating constraints, by adjusting zone flow rates. Because this problem is nonconvex, we propose two methods to (approximately) solve it and to design the real-time control. In the first method, we present a convex relaxation approach to solve an approximate version of the steady-state optimization problem, where the heat transfer between neighboring zones is ignored. We prove the tightness of the relaxation and develop a real-time decentralized algorithm to regulate the zone flow rate. In the second method, we introduce a mild assumption under which the original optimization problem becomes convex, and then a real-time distributed algorithm is developed to regulate the zone flow rate. In both cases, the thermal dynamics can be driven to equilibria which are optimal solutions to those associated steady-state optimization problems. Finally, numerical examples are provided to illustrate the effectiveness of the designed control schemes.