Categorical Semantics of Cyber-Physical Systems Theory

Cyber-physical systems require the construction and management of various models to assure their correct, safe, and secure operation. These various models are necessary because of the coupled physical and computational dynamics present in cyber-physical systems. However, to date the different model views of cyber-physical systems are largely related informally, which raises issues with the degree of formal consistency between those various models of requirements, system behavior, and system architecture. We present a category-theoretic framework to make different types of composition explicit in the modeling and analysis of cyber-physical systems, which could assist in verifying the system as a whole. This compositional framework for cyber-physical systems gives rise to unified system models, where system behavior is hierarchically decomposed and related to a system architecture using the systems-as-algebras paradigm. As part of this paradigm, we show that an algebra of (safety) contracts generalizes over the state of the art, providing more uniform mathematical tools for constraining the behavior over a richer set of composite cyber-physical system models, which has the potential of minimizing or eliminating hazardous behavior.