Hetero-functional Graph Theory

Abstract

Hetero-functional graph theory is an intellectual fusion of model-based systems engineering and network science. This chapter provides an exposition of hetero-functional graph theory in terms of its constituent mathematical models and how they relate to their counterparts in SysML. These models are: (1) the System Concept, (2) the Hetero-functional Adjacency Matrix, (3) the Controller Agency Matrix, (4) the Controller Adjacency Matrix, (5) the Service as Operand Behavior, (6) the Service Feasibility Matrix, and (7) the System Adjacency matrix. The first two models are assumed to be universal and apply to all types of engineering systems. They form the structural model. The last four apply when it is necessary to differentiate systems. Models 3 and 4 constitute the system control model. Together, they differentiate systems based upon the structure of their control and decision-making. Models 5 and 6 constitute the service model. They differentiate systems based upon the behavior of their operands. These six models are then ultimately coupled together for holistic analysis of cyber-physical engineering systems. When integrated together, these models constitute the final product of hetero-functional graph theory: the System Adjacency Matrix.