I will now turn to the question of what constitutes the foundations of CPS. With foundations I will refer to theory in the sense of well-confirmed models, procedures and explanations that help in performing design as well as in understanding and analyzing existing CPS – i.e. as an engineering perspective to foundations. A theory for CPS should provide us with “tools” to predict behaviors and properties of CPS as a function of design descriptions. By changing certain design parameters we should for example be able to understand how changes propagate and influence other parts and properties of a CPS.

A key opportunity and also key challenge for CPS, is their heterogeneity, exploiting multiple technologies and the synergies among the physical and cyber worlds. The CPS approach is “compositional” . Unfortunately this does not align with how science and engineering have progressed. In dealing with an expanding scope of knowledge, progress has instead been characterized by increasing depth and specialization, resulting in many specialty disciplines. As a consequence, there is no single CPS theory available today (this challenge is by the way shared by many contemporary fields today!).

The behavior of a CPS is multifaceted. To understand and design a CPS, we will most likely have to resort to a large number of theories including Newtonian laws of motion, control and dynamic systems, hybrid systems, real-time, programming, digital logic, information theory, cognitive science (when CPS involves humans), etc. In addition, we will be needing theory related to cross-cutting theories and engineering foundations such as those concerned with security, reliability and safety.

The inherent complexity of a CPS, likewise implies that engineering methodologies will involve a number of ways to divide and conquer a complex problem into separate pieces (parts, or steps part of engineering processes), with guidelines for integrating them. The challenge here lies in having foundations to support both the decomposition as well as the composition (the integration).

The properties of a CPS appear as a result of the component, software and physical system properties and their interactions. Since a CPS typically involves tight integration among components and various technologies, intricate relationships will result which impact system level aspects/properties such as functionality, performance, safety, security, availability and interoperability. Changes in some of the component level properties, or the composition of components, is likely to affect multiple system level properties. This leads to tensions and necessitates trade-offs assuming that these interrelations are understood and can be managed). The challenge of CPS engineering also becomes an organizational challenge since it is beyond the capabilities of a single person to develop an advanced CPS (the design of a modern car will involve thousands of engineers).

Systems Engineering (SE) has a goal to deal with complex systems, and as such help to deal with composition and integration. However, SE was developed initially mainly to target large scale physical systems, and there is a realization that it needs to evolve to better embrace the cyber dimensions.

There is thus a great need for addressing the foundations of CPS, in innovating foundations that cut across the multiple facets of CPS. The involved challenges and opportunities for further work include to develop a better understanding of facets of CPS complexity, composability of CPS (principles for achieving desired behaviors, properties and trade-offs), dealing with Cyber-Physical Systems of Systems (including cross-organizational interactions), human-centered design of CPS, and handling AI as a novel ingredient in CPS.

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