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.

本文设计了分散、分布式的实时控制方案，旨在平衡用户舒适度和节能，并在不测量或预测外部干扰的情况下实现。通过调整区域流量，我们提出一个热动力学建模和稳态资源分配问题的优化方法，可以最小化区域温度和建筑能耗之间的总偏差，同时考虑实际操作限制。根据该问题的非凸性质，我们提出两种方法来解决它并设计实时控制。在两种情况下，都可以将热动力学驱动到最优解并平衡节能和舒适度。