EAGER: A Categorical Approach to Systems Modeling for Systems Engineering

这项探索性研究早期概念基金（EAGER）支持使用范畴理论（CT）的基础研究，为大型工程系统开发中的系统性能建模创建数学框架。准确有效的系统性能建模对系统工程项目的决策至关重要。系统组件和子系统的各种不可通约模型（物理的、逻辑的和人的）与理解作为一个整体的系统相关。当前实践的一个主要不足是无法使用不同的形式（包括微分方程、逻辑和随机模型）在不同的抽象层次上构建模型来无缝地模拟和研究系统行为。本项目将研究一种基于CT的新方法，该方法有望解决这一缺点并改变系统工程的实践。对系统性能更好的预测将导致在包括但不限于航空航天、医疗保健、国防和能源等领域中性能更好的工程系统。该项目的技术进步将具体体现在稳定的智能配电系统的设计中。当前的系统工程实践依赖于信息模型，如SysML、BPML等语言来组织系统工程中涉及的众多模型及其生成的数据。这个项目的目标是证明CT作为跨系统建模中使用的各种数学形式化的桥梁元形式化。这项研究将为基于ct的系统建模提供基础结果，这将为系统工程提供新的工具和方法。CT提供的形式语言可以超越单个的建模形式，并为系统工程师提供创建系统的组合模型的能力，以便跨尺度进行推理。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（电力负载和发电）和必须考虑多个时间尺度（毫秒，分钟和小时）的运行。在这个试验台问题上的成功将为进一步研究基于ct的系统建模提供有力的证据。

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.