Autonomy Talks - Georgios Bakirtzis: Compositional Cyber-Physical Systems Theory

Autonomy Talks - 11/01/2021
Speaker: Georgios Bakirtzis, University of Virginia
Abstract: In the modeling and analysis of CPS the word composition appears in many different contexts and may refer to different things. In systems engineering we occasionally use the term composite system in a formal but relaxed sense. On the contrary, the term compositionality is not a formal term, rather the general characteristic of an analysis that ensures that the behavior of the whole is determined by the behavior of its building blocks.
In this talk we will start with some elements of compositionality in cyber-physical systems theory and show how category theory can formalize those notions explicitly. Category theory is one context where the meaning of composition is formal and refers to something specific, namely the partial operation on morphisms of a category. We formalize categorically the notion of composite system in this work using the systems-as-algebras framework in the wiring diagram category.
A combination of models is often used to assure metrics such as safety and security as well as dynamics and control. The categorical formalization of composition gives rise to a unification of (a subset) of requirements, system behaviors, and system architectures in a manner that is traceable. We will show how the notion of functoriality - structure preserving maps between categories - can give concrete meaning to abstraction and refinement in cyber-physical system models, which can assist with the specification (and eventually validation) of increasingly complex systems.
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