Humans-in-the-loop: A Game-Theoretic Perspective on Adaptive Building Energy Systems

Efficient building energy management has attracted a great interest in diverse research areas due to significant potential energy savings. A remaining challenge is how to combine the efforts of engineers on improving the energy management system with approaches developed by social scientists to integrate the occupants actively in the energy management system. This paper proposes the formulation of a game between the building energy management system and occupants to agree on room temperature comfort bounds. Under mild assumptions on the cost functions of the occupants, we show that a generalized Nash equilibrium exists and it can be shown to equal the social optimum. The alternating direction method of multipliers is used to solve the resulting consensus optimization problem in a distributed way, with the building management system as coordinator. An advantage of the proposed method is that the building energy management system does not need to rely on an explicit model of the occupant behavior but due to the game theoretic approach, indirectly receives an adapted model at each iteration. An extensive numerical study demonstrates the efficacy of the proposed approach.