EAGER: A Categorical Approach to Systems Modeling for Systems Engineering

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

This EArly-concept Grant for Exploratory Research (EAGER) grant supports fundamental research into the use of Category Theory (CT) to create a mathematical framework for systems performance modeling in development of large engineered systems. Accurate and effective modeling of system performance is critical to inform decision making in systems engineering projects. A variety of incommensurable models (physical, logical and human) of system components and subsystems are relevant to understanding the system as a whole. A major shortfall of current practice is an inability to compose models to simulate and study system behavior seamlessly at different levels of abstraction using different formalisms including differential equations, logic and stochastic models. This project will investigate a new approach based on CT that promises to address this shortcoming and transform the practice of systems engineering. Better predictions of system performance will lead to better-performing engineered systems in areas that include, but are not limited to, aerospace, healthcare, defense, and energy. The technical advances of this project will be demonstrated specifically in the design of stable smart power distribution system. Current systems engineering practice relies on information models such as SysML, BPML and other languages to organize the numerous models involved in systems engineering and the data they generate. The objective of this project is to demonstrate CT as a bridging meta-formalism across the variety of mathematical formalisms used in the modeling of systems. This research will contribute fundamental results in CT-based systems modeling that will enable new tools and approaches for systems engineering. The formal language afforded by CT can transcend the individual modeling formalisms and offer systems engineers the ability to create a compositional model of the system for inferencing across scales. The smart power distribution system problem exhibits many challenging aspects, including stochasticity (in power loading and generation) and operation that must consider multiple time scales (milliseconds, minutes, and hours). Success on this testbed problem will provide compelling evidence that further study of CT-based systems modeling is warranted.