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design new ones, and define their fundamental limits.

Example 1.1 Chocolate cake. You would like to prepare the chocolate cake you ate in your childhood, whose recipe you found in the Internet. This instructs you how to make it. If you follow the instructions, you will have the cake you wish but without knowing why that specific combination of elements and the processes of mixing and cooking can produce such a cake. If you decide to investigate the recipe, you will find that different elements are compatible for chemical reasons, and, after processing then in a specific way, such a combination will have the desired flavor and structural characteristic. Based on this abstraction, you can now (i) understand the reasons why the recipe works, (ii) propose modifications to the recipe to make the cake fluffier or moister, and (iii) create a vegan version of the cake by finding replacement for milk, butter, and eggs.

      This example serves as a very simplified illustration of the difference between technical knowledge (know‐how) and scientific knowledge. We are going to discuss sciences and scientific practice in more detail when pinpointing the philosophical position taken throughout this book. At this point, though, we should return to our main concern: the need for a general theory that conceptualizes CPSs. Like the particular chocolate cake, the existence of smart grids or cities, or even fully automated production lines neither precludes nor requires a general theory. Actually, their existence, the challenges in their particular deployments, and their specific operation can be seen as the necessary raw material for the scientific theory that would build the knowledge of CPSs as a symbolic (general, abstract) object. This theory would provide the theoretical tools for orienting researchers, academics, and practitioners with objective knowledge to analyze, design, and intervene in particular (practical) realizations of this symbolic object called CPS.

      Without advancing too much too soon, let us run a thought experiment to mimic a specific function of smart meters as part of the smart electricity grid – one of the most well‐known examples of CPS. Consider the following situation: the price of electricity in a household is defined every hour and the smart meter has access to this information. The smart meter also works as a home energy management system, turning on and off some specific loads or appliances that have flexibility in their usage as, for instance, the washing machine or the charging of an electric vehicle (EV). If there is no smartness in the system, whenever the machine is turned on or the EV is plugged in, they will draw electric energy from the grid. With the smart meter deciding when the flexible load will turn on or off based on the price, the system is expected to become smart overall: not only flexible loads could be turned on when there is a low price (leading to lower costs to the households) but this would also help the grid operation by flattening the electricity demand curve (which has peaks and valleys of consumption ideally reflected by the price).

This seems too good to be true, and it indeed is! The trick is the following. The electricity price is a universal signal so that all smart meters see the same value. By facing the same price, the smart meters will tend to switch on (and then off) the loads at the same time, creating a collective behavior that would probably lead to unexpected new peaks and valleys in demand that cannot be predicted by the price (which actually reflects past behaviors, and not instantaneous ones). The adage the whole is more than the sum of its parts then acquires a new form: the smartness of the smart meters can potentially yield a stupid grid [2]. This outcome is surprising since individually everything is working as expected, but the system‐level dynamic is totally undesirable. How to explain this?

      The smart grid, as we have seen before, is considered a CPS where physical processes related to energy supply and demand are reflected in the cyber domain by a price signal that serves as the basis for the decisions of smart meters, which then modify the physical process of electricity demand by turning on appliances. However, the smart meters described above are designed to operate considering the grid dynamics as given so that they individually react to the price signal assuming that they cannot affect the electricity demand at the system level. If several of such smart meters operate in the grid by reacting to the same price signals, they will tend to have the same decisions and, consequently, coordinate their actions, leading to the undesirable and unexpected aggregate behavior. This is a byproduct of a segmented way of conceptualizing CPSs, which overestimates the smartness of devices working individually while underestimating the physical and logical (cyber) interrelations that constitute the smartness of the CPS.

Figure 1.2 illustrates this fact. The electricity hourly price is determined from the expected electricity demand following the indication of arrow (a). The smart meters would lead to a smart grid if the spikes in consumption would be flattened, as indicated by arrow (b). However, due to the unexpected collective effect of reactions to the hourly price, the realized demand has more spikes than before, creating a stupid grid. This is pointed by arrow (c).

Figure 1.2 Operation of smart meters that react to hourly electricity price. Arrow (a) indicates that the hourly price is a function of the expected electricity demand. Arrow (b) represents the planned outcome of demand response, namely decreasing spikes. Arrow (c) shows the realized demand as an aggregate response to price signals, leading to more spikes.

      At all events, coordination and organization of elements working together are old problems under established disciplines like systems engineering and operational research. However, those disciplines are fundamentally based on centralized decision‐making and optimal operating points; this is usually called a top‐down approach. In CPSs, there is an internal awareness and a possibility of distributed or decentralized decision‐making based on local data and (predefined or learned) rules co‐existing with hierarchical processes. Hence, CPSs cannot be properly characterized without explicit definition of how data are processed, distributed, and utilized for informed decisions and then actions. A general (scientific) theory needs to be built upon the facts that CPSs have internal communication–computation structures with specific topologies that result in internal actions based on potentially heterogeneous decision‐making processes that internally modify the system dynamics. Some of these topics have been historically discussed within control and information theories, as well as cybernetics.

1.3 Historical Highlights: Control Theory, Information Theory, and Cybernetics

Control theory refers to the body of knowledge involving automatic mechanisms capable of self‐regulating the behavior of systems. Artifacts dating back to thousands of years indicate the key idea behind feedback control loop. The oldest example is probably the water clock where inflow and outflow of water is used to measure time utilizing a flow regulator, whose function is [3]: “(…) to keep the water level in a tank at a constant depth. This constant depth yielded a constant flow of water through a tube at the bottom of the tank which filled a second tank at a constant rate. The level of water in the second tank thus depended on time elapsed.” Other devices based on the same principle have also been found throughout history. With the industrial revolution in the 1700s, different types of regulators and governors have appeared as part of the unprecedented technological development. It was desirable for the new set of machinery like windmills, furnaces, and steam engines to be controlled automatically. Hence, more and more solutions based on feedback and self‐regulation started to be developed. At that point, the development was of a practical nature, by trial‐and‐error. In a groundbreaking work by J. C. Maxwell (also the “father” of electromagnetism) from 1868 [4], the first step to generalize feedback control as a scientific theory was taken. Maxwell analyzed systems that employ governors by linearized differential equations to establish the necessary conditions for stability based on the system's characteristic equation. This level of generalization that states fundamental (mathematical) conditions that apply to all existing and potentially future objects of the same kind (i.e. feedback control systems) is the heart of the scientific endeavor of control theory.

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