Tags:almost everywhere, differential temporal dynamic logic, hybrid systems and proof calculus

Abstract:

Some hybrid systems models are unsafe for mathematically correct but physically unrealistic reasons. For example, mathematical models can classify a system as being unsafe on a set that is too small to have physical importance. In particular, differences in measure-zero sets in models of cyber-physical systems (CPS) have significant mathematical impact on the mathematical safety of these models even though differences on measure-zero sets have no tangible physical effect in a real system. We develop the concept of ``physical hybrid systems'' to help reunite mathematical models with physical reality. We modify a hybrid systems logic (differential temporal dynamic logic) by adding a first-class operator to elide distinctions on measure-zero sets of time within CPS models. This approach facilitates modeling since it admits the verification of a wider class of models, including some physically realistic models that would otherwise be classified as mathematically unsafe. We also develop a proof calculus to help with the verification of physical hybrid systems.