CPS foundations.

This paper argues that cyber-physical systems present a sub-stantial intellectual challenge that requires changes in both theories of computation and dynamical systems theory. The CPS problem is not the union of cyber and physical problems, but rather their intersection, and as such it demands models that embrace both. Two complementary approaches are identified: cyberizing the physical (CtP) means to endow physical subsystems with cyber-like abstractions and interfaces; and physicalizing the cyber (PtC) means to endow software and network components with abstractions and interfaces that represent their dynamics in time.