Abstract
In this paper, we present a framework for modeling certain classes of cyber-physical systems using graph-theoretic thinking augmented by ideas from the field of behavioral systems theory. 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). Motivated by building thermal example, we present a framework for dynamic graphs and dynamic consensus networks. This framework introduces the idea of dynamic degree, adjacency, incident, and Laplacian matrices in a way that naturally extends these concepts from the static case. From this, we can easily define equivalent concepts of the dynamic consensus networks. Then we show how a behavioral systems approach can be used to develop kernel relationships between all system variables in dynamic graphs as typified by building thermal models. We discuss how such relationships can be used to analyze these systems’ properties, focusing on controllability. The ideas developed for dynamic graph theory lead to developing a controllability analysis methodology for dynamic consensus networks in conjunction with the behavioral approach. We then developed the controllability conditions for the general dynamic networks, such as identical LTI nodes with dynamic edges or even in the more general case with heterogeneous nodes.
Recommended Citation
Lashhab, Fadel; Abdulgader, Musbah; and Zargelin, Omar A.
(2024)
"A Dynamic Graph-Based Systems Framework for Modeling, and Control of Cyber-Physical Systems Typified by Buildings,"
American Journal of Science & Engineering (AJSE): Vol. 2:
Iss.
1, Article 1.
Available at:
https://research.smartsociety.org/ajse/vol2/iss1/1