We describe a social game that we designed for encouraging energy efficient behavior amongst building occupants with the aim of reducing overall energy consumption in the building. Occupants vote for their desired lighting level and win points which
are used in a lottery based on how far their vote is from the maximum setting. We assume that the occupants are utility maximizers and that their utility functions capture the tradeoff between winning points and their comfort level. We model the occupants as non-cooperative agents in a continuous game and we characterize their play using the Nash equilibrium concept. Using occupant voting data, we parameterize their utility functions and use a convex optimization problem to estimate the parameters. We simulate the game defined by the estimated utility functions and show that the estimated model for occupant behavior is a good predictor of their actual behavior. In addition, we show that due to the social game, there is a significant reduction in energy consumption.
Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase
this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well posed we assume that the sought input lies in some known linear subspace.
