A Dynamic Graph-Based Systems Framework for Modeling, and Control of Cyber-Physical Systems Typified by Buildings

In this chapter, we present a framework for modeling certain classes of cyber-physical systems using graph-theoretic thinking. The cyber-physical systems we consider are typified by buildings. We show that the thermal processes associated with a building can be represented as a graph in which (1) the node variables (temperature and heat flows) are governed by a dynamic system and (2) interconnections between these nodes (walls, doors, windows) are also described by a dynamic system. In general, we call a collection of such nodes and interconnections a dynamic graph (dynamic consensus network).Driven to explore this by developing thermal examples, this study outlines a practical framework for dynamic consensus networks and dynamic graphs. In a manner that seamlessly extends these concepts from the static cases, we will explore the combination of dynamic degrees, adjacency, Laplacian matrices, and incident matrices. With these conceptual tools, one can quickly identify equivalent concepts of dynamic consensus networks.