A Clock-Based Specification of Cyber-Physical Systems

In cyber-physical systems, the elapse of time becomes the most important property of system behavior, and time is central to predicting, measuring, and controlling properties of the physical world. A cyber-physical system is composed of two interacting subsystems: a cyber system and a physical system. The behavior of the cyber system is controlled by the execution of programs on a distributed digital computer system, while the laws of physics control the behavior of the physical system. The different models of time—continuous physical time in the physical system versus discrete execution time in the cyber system and the impossibility of perfect synchronization of the physical clocks of the nodes of a distributed computer system, lead to interesting phenomena concerning the joint behavior of these two subsystems. The chapter describes the case studies in applying clock theory to the production cell. The clock theory described is very simple, in that it models clocks as potentially infinite lists of reals. Xeno’s paradox and similar problems are avoided by specifying limits on clock rates, which effectively means that the model sits somewhere between a discrete synchronous model and a fully dense continuous-time model as assumed by some other formalisms. The case study of the specification of the production cell shows that using clock theory to specify cyber-physical systems can give a more detailed description of the every subsystem and give a much more considerate observation of the time line and sequence of every event.