EAGER: A Categorical Approach to Systems Modeling for Systems Engineering

这项早期概念探索性研究(AGUGER)拨款支持使用范畴理论(CT)来创建大型工程系统开发中系统性能建模的数学框架的基础研究。准确而有效的系统性能建模对于系统工程项目中的决策至关重要。系统组件和子系统的各种不可通约的模型(物理的、逻辑的和人类的)与理解整个系统有关。当前实践的一个主要缺陷是无法使用包括微分方程、逻辑和随机模型在内的不同形式来构建模型来无缝地模拟和研究不同抽象级别的系统行为。这个项目将研究一种基于CT的新方法，它有望解决这一缺陷，并改变系统工程的实践。对系统性能的更好预测将在包括但不限于航空航天、医疗保健、国防和能源等领域带来更好的工程系统性能。目前的系统工程实践依赖于SysML、BPML等语言等信息模型来组织系统工程中涉及的众多模型及其生成的数据。这个项目的目标是展示CT作为跨越系统建模中使用的各种数学形式主义的桥梁的元形式主义。这项研究将有助于在基于CT的系统建模方面取得基本成果，从而为系统工程提供新的工具和方法。CT提供的形式化语言可以超越个人的建模形式化，并为系统工程师提供创建系统的组合模型以进行跨尺度推理的能力。智能配电系统问题表现出许多具有挑战性的方面，包括随机性(在电力负荷和发电中)和必须考虑多个时间尺度(毫秒、分钟和小时)的运行。这个试验台问题的成功将提供令人信服的证据，证明基于CT的系统建模的进一步研究是必要的。

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.