Graph based multi-scale analysis of building system transport models

This paper offers a framework for multi-scale analysis, modeling, and control design for energy efficient building systems models. Our unique approach is to conceptualize the building systems problems as dynamics (convection-diffusion equations) on a building graph. While the original graph - that resolves the smallest of the scales - is complex, we use the coarse spatio-temporal scales associated with any particular control objective to drive towards an effective (low-dimensional) representation of dynamics on the graph. The key idea here is to use the Perron-Frobenius (P-F) operator for averaging the fast time scales that would decay on account of diffusion in the problem. The framework is presented with aid of a one-room and two-room model problems.