Simultaneous identification of linear building dynamic model and disturbance using sparsity-promoting optimization

Abstract

We propose a method that simultaneously identifies a control-oriented model of a building’s temperature dynamics and a transformed version of the unmeasured disturbance affecting the building. Our method uses ℓ1-regularization to encourage the identified disturbance to be approximately sparse, which is motivated by the slowly-varying nature of occupancy that determines the disturbance. The proposed method involves solving a feasible convex optimization problem that guarantees that the identified black-box model, a linear time-invariant system, possesses known properties of the plant, especially input–output stability and positive DC gains. These features enable one to use the method as part of a self-learning control system in which the model of the building is updated periodically without requiring human intervention. Results from the application of the method on data from a simulated and real building are provided.