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Compositional Models for Complex Systems 245

or diagnose the behavior of such a system we may need to explore psychol-
ogy, probability, dynamics, and logic. Moreover, each element has its own
logic of interaction. Sensors can support many subscribers whereas most
actuators allow only one operator (at a time); humans are unpredictable
in ways both good and bad. There are also other, less obvious components
in our systems such as logical resources like encryption keys and personal
data, which must be regarded as components of our systems if we hope
to enforce concerns like information security.

13.2.2 Open Interaction

A central feature of complex systems is that components are expected to
interact, and through that interaction unlock value and efficiency. More spe-
cifically, components provide interfaces, both physical and logical, which
may be coupled into a wide variety of different arrangements. Thus to
understand the behavior of an IoT or AI system it is not enough to describe
its components; we must also specify the architecture that wires those com-
ponents together. In contrast to traditionally engineered systems, composi-
tion of modern systems will often be provisioned on an ad hoc basis in
reaction the operational environment, sharpening the need for predictive
tools for system behavior and security. For example, the conception and
design of Smart Grid with distributed energy resources would require
on-demand provisioning of electric power by tapping additional generation
resources or by reducing demand in power-consuming devices to dynam-
ically balance supply and demand.

13.2.3 Multiplicity of Perspectives

There is a tremendous range of viewpoints from which we may wish to con-
sider a given system. Some of these are based on scale; an IoT system may
range from a single individual (personal devices) to a building (HVAC) to a
city or region (Smart Grid). This system-of-systems aspect of the IoT means
that its local behavior may depend on any of these levels. Legal regulations
introduce a new set of perspectives, including safety or privacy requirements
as well as reporting for regulatory oversight. Organizationally and econom-
ically speaking, the user of a component may not be its owner, and these two
actors may be connected through a third-party platform. Systems models
must embed all of these individual perspectives, but should also allow for
the integration of multiple perspectives in order to analyze interactions
across multiple concerns (Subrahmanian, Westerberg, & Podnar, 1989).