Problem formulations for systems of systems

The purpose of this paper is to formulate mathematical definitions for key concepts in the area of systems of systems, and to do this in a way that alternative formulations with associated algorithmic advantages might be revealed. The first step to a mathematical study of a problem is to be able to write it down in carefully defined terms. Generally we assume that a system of systems has a central authority and subsystems. The taxonomy we propose is related to how much or little control, including none at all, is wielded by the central authority, and how interactions between subsystems are handled.