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

Fadel M Lashhab

doi:10.5772/intechopen.98657

Abstract

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.

Highlights

We present a detailed study of modeling thermal processes in buildings as directed, dynamic graphs, beginning with a simple two-room model and transitioning to multiple interconnected rooms
This Chapter studied a generalization of consensus network problems whereby the network edges’ weights are no longer modeled as static gains. They are represented as dynamic systems coupling the nodes. We call such networks dynamic consensus networks because, under some conditions, all node variables converge to a common value called a consensus
We presented examples of how dynamic graphs can arise in applications

Summary

Introduction

We present the analysis and design of cyber-physical systems using graph-theoretic ideas. A building may be viewed as a hybrid system where a physical process (the structure itself) has been augmented with a hardware infrastructure (sensors and actuators) and a cyber-infrastructure (communication and decision nodes) Such overlaid heterogeneous systems with constrained connectivity and interaction between the different layers present challenges and system optimization and control opportunities. We show how a behavioral systems approach can develop kernel relationships between all system variables in dynamic graphs typified by building thermal models Using these kernel relationships, we consider the controllability analysis of such systems. By the notation “dynamic systems,” we mean that linear ordinary differential equations (LODEs) are described as relationships between the system variables We call such networks dynamic consensus networks because all the node variables converge to a common value called a consensus value under some conditions. One can define equivalent concepts of dynamic interconnection matrices and dynamic consensus networks

Modeling a thermal process in a building as a directed dynamic graph

Two rooms connected by a wall

Several interconnected rooms

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Dynamic graphs definitions

Conclusion