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2.1 System in [1] (1) A regularly interacting or interdependent group of items forming a unified whole; (2) an organized set of doctrines, ideas, or principles usually intended to explain the arrangement or working of a systematic whole; (3a) an organized or established procedure; (3b) a manner of classifying, symbolizing, or schematizing; (4) harmonious arrangement or pattern; (5) an organized society or social situation regarded as stultifying or oppressive.

      It is clear the meaning I used to answer to my daughter is (1). At this point, two remarks are needed. First, not everything that is a regularly interacting or interdependent group of items forming a unified whole constitutes a system. For example, a clock, a car, or a computer are usually considered systems, while open markets or football teams are not (even though they might). This relatively arbitrary daily usage of the word shall be abandoned later in this chapter. The second remark is that the different meanings of the same word may create a series of confusion. While the meaning (1) mostly refers to the concrete reality, (2) and (3) seem to refer to symbolic domains, (4) and (5) are fuzzier and more subjective. Since this book is about engineering, (1) is the most appropriate meaning as our starting point.

      With those warnings given, we are almost ready to transform the word “system” – our first raw material – into a concept that will become operational in the proposed theory of cyber‐physical systems. Before we begin, though, it is important to describe how we will proceed. The first move is to provide a descriptive technical definition of what a system is following the well‐established discipline Systems Engineering [2]. After this presentation, we can finally specify how it is possible to demarcate and articulate a particular functioning system with respect to its environment.

2.2 Systems Engineering

      This section revisits the pedagogical exposition of the main technical terminology employed in Systems Engineering following the textbook Systems Engineering and Analysis [2]. The definition below states its answer to the question what is a system?

Definition 2.2 System A system is a set of components whose individual operating parts have specific attributes that are combined to form certain relations to perform one or few specific functions.

      This definition is constructed upon four concepts:

      1 Components: the elementary material parts – the building blocks – of the system.

      2 Attributes: the properties of the components, or of the system as a whole.

      3 Relations: the connections between components.

      4 Function(s): what the system needs to accomplish.

      It is quite straightforward to think in these terms. There are some specific pieces that are combined to form a whole that, if put together in such an organized form, can perform a predetermined task. Think about the do‐it‐yourself trend of building furniture, or even a house.

      It is also important to point out that systems are always (directly or indirectly) related to dynamical processes. In other words, systems change. These changes usually refer to the state (situation) of the system at a specific point in time and in space. A series of changes in its state is called behavior. A process then refers to a sequence of behaviors. The function of the system is the outcome of a process or a series of processes.

      It should be clear that the function of a particular system cannot be performed by any of its individual components alone, reminding us that the system is more than the sum of its parts. Roughly speaking, each component has its own role based on its attributes and interrelations. Depending on the role in the system, the different components can be classified into one of the following categories.

      1 Structural components: The (quasi‐)static parts of the system.

      2 Operating components: The parts that perform the processing.

      3 Flow components: Whatever (e.g. material, data or energy) is processed by the systems.

Structural components usually provide the support for the operating components to process the flow components. Before entering the system, the flow components are called inputs; the flow components that leave the system after processing are called outputs. The process of transformation from inputs to outputs that is performed inside the system always requires a motive force, either internal or external to it. Note, though, that not all systems have such a transformation process as their main function; there are systems whose function is transportation (i.e. flow of materials or data), or structural support for other systems to work (i.e. a highway, a bridge, or a railway). Nonetheless, all functioning systems (actively or passively) do work in a physical sense, and thus, energy is always converted in, by, or through systems. Systems may also function in a hierarchy: components can be systems in their own right, but, with respect to another broader system, they are simply subsystems. There also exist subsystems composed of other subsystems, and such a regression may go on as needed.

      The following example illustrates all that has been discussed so far in this chapter.

      Example 2.1 Car as a system. A car is composed of several different components from the three classes as, for example:

      1 Structural: Chassis, windows, springs, and wheels.

      2 Operating: Engine, brake, fuel pump, and radiator.

      3 Flow: Electricity, diesel, air, and persons.

      These and all other possible components of the car together are combined and designed to function as a whole system in order to perform a specific function: transporting persons from one place to another. A car may be either in a moving state or in a static state. The relation between the attributes of two components of the car, engine (attribute: converting thermal energy into kinetic energy) and wheels (attribute: using the kinetic energy converted by the engine to move the car), determines the behavior of the car over time and space. This relation is fundamental for the car to accomplish its function. The wheels and the engine are subsystems of the car. For example, the engine analyzed as a system functions by processing fuel (its input) in order to transform it into heat that will be converted into motion (its output). While the engine is a subsystem of the car, the car can also be analyzed as a subsystem of a transportation system.

      What is of utmost importance for analyzing and engineering a system is to demarcate its boundaries, limits, and scope considering its particular function(s) while articulating it with its external world, its environment. In this sense, the focus needs to be on functioning systems, or systems that have potential to function. This topic will be the focus of the next section.

2.3 Demarcation of Specific Systems

      The definition of a particular system is usually arbitrary or assumed as given. When someone talks about a car, anyone listening should have a very clear idea about that system. But, this might be a trick: is a car without an engine, or wheels, still a car? Similar kinds of discussions are very common in other domains as well. For example: should an oat‐based drink be called oat milk?

In the legal domain, this definition is normative, usually as result of a deliberative process so that a definition can be imposed to indicate which is the correct word to name a given thing. The same happens with the word “car.” Each country has its own legal definition of what is considered a “car” indicating who is eligible to drive, or what taxes are to be paid. However, as we have discussed in the previous chapter, scientific concepts are different from words used in other practices: the former exist in a specific theoretical discourse whose meaning is completely defined by the formal structure of the theory they are part of. The scientific meaning of the word “car” then needs to be very well‐defined if it is to be considered a scientific concept. The question remains: how could such a theoretical

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