EAGER: A Categorical Approach to Systems Modeling for Systems Engineering

EARLY概念探索性研究资助（EAGER）资助支持使用范畴理论（CT）的基础研究，以创建大型工程系统开发中系统性能建模的数学框架。准确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分割的模型（物理，逻辑和人类）与理解整个系统有关。当前实践的一个主要不足是无法使用不同的形式主义（包括微分方程、逻辑和随机模型）在不同的抽象层次上无缝地组成模型来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。更好的系统性能预测将导致在包括但不限于航空航天、医疗保健、国防和能源等领域的工程系统性能更好。该项目的技术进步将在稳定的智能配电系统的设计中得到具体展示。当前的系统工程实践依赖于信息模型，如SysML，BPML和其他语言来组织系统工程中涉及的众多模型及其生成的数据。 这个项目的目的是证明CT作为一个桥接元形式主义的各种数学形式主义用于系统建模。这项研究将有助于基于CT的系统建模，将使新的工具和方法的系统工程的基本成果。CT提供的形式语言可以超越单个建模形式主义，并为系统工程师提供创建系统的组合模型的能力，以进行跨尺度的推理。智能配电系统问题具有许多挑战性的方面，包括随机性（在功率加载和发电）和操作，必须考虑多个时间尺度（毫秒，分钟和小时）。这个试验台问题的成功将提供令人信服的证据，进一步研究基于CT的系统建模是必要的。

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.