Modeling and Control of Ceovolutionary Network Formation with Applications to Finishing Processes for 3D Printed Components

网络表示允许通过提供所考虑的系统内实体之间的成对关系的明确表征来深入理解自然和技术系统的动态。例如，使用网络来表示社区中个人之间的身体接触，可以比假设人口均匀混合的标准模型更精确地表示传染病爆发动态。然而，网络并不是凭空出现的，考虑到系统的动态性质，它们的统计特性往往会随着时间的推移而演变。该项目解决了网络科学和控制理论领域的基本问题，即现实世界的网络是如何产生的，它们如何与环境共同进化，以及它们如何受到干扰。该项目的理论方面将通过控制3D打印中材料表面的局部精加工过程的实验线程进行评估，并在一定程度上受到激励。亚微米级的材料表面可以被认为是一张起皱的纸，上面有粗糙的表面和允许网络表示的孔隙。精加工过程旨在通过研磨作用将粗糙表面（断开的网络）有效地转变为光滑表面（高度连接的网络）。目前，通常用于在3D打印部件上赋予所需表面特性的精加工和后处理技术消耗了总周期时间的20-70%。精加工过程的效率提高和自动化可以克服工业采用这项技术的主要障碍。网络在真实的世界中的形成和变化不仅仅是由于其内部实体之间的相互作用（即，节点），而是来自它们与环境的动态耦合和共同进化。本研究旨在实现以下科学贡献：（1）具有内生动力过程和战略节点级决策的新型网络形成模型，以及表征延迟和临界反馈对新兴网络结构的影响; B）控制网络形成的理论框架，为决策提供最佳干预，动态过程或网络结构通过外部代理，以便形成所产生的网络特征; c）在精加工过程中表面形态演变的一致网络表示，以及高效且保证所需表面性质的自动化局部精加工过程。网络形成过程建模的关键技术新奇是引入环境动态和节点行为的延迟效应，这产生了一组丰富的动态，质疑基本网络形成模型的鲁棒性。我们建议利用最近的影响最大化和最优控制与Kullback-Leibler控制成本的工作，提供一个控制理论框架，有效地获得所需的网络结构的非线性动力学的共同进化网络。我们的验证工作有望展示所提出的理论框架如何在新的应用领域中具有变革性，例如，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Network representations allow a deep understanding of the dynamics of natural and technological systems by providing explicit characterization of pairwise relations between entities within the system in consideration. For instance, using networks to represent physical contacts among individuals in a community can provide a more precise representation of an infectious disease outbreak dynamics than standard models where homogeneous mixing of the population is assumed. However, networks do not appear out of thin air and their statistical properties tend to evolve over time given the dynamic nature of the systems. This project addresses the fundamental issues that are at the nexus of fields of network science and control theory, on how real-world networks arise, how they co-evolve with the environment, and how they can be perturbed. Theoretical aspects of this project will be assessed, and in part are motivated, by an experimental thread in controlling localized finishing processes of material surfaces in 3D printing. A material surface at the sub-micrometer level can be thought of as a wrinkled paper with asperities and pores that admits network representations. A finishing process aims to efficiently transition a rough surface (disconnected network) into a smooth surface (highly connected network) through abrasive action. Currently, finishing and post-processing techniques, commonly used to impart desired surface characteristics on 3D printed components, consume 20-70% of the total cycle time. Efficiency gains in and automation of finishing processes can overcome this major impediment to the industrial adoption of this technology. Networks form and change in the real world not just due to the interactions among their internal entities (i.e., nodes) but from their dynamic coupling and coevolution with the environment. The research aims to achieve the following scientific contributions: a) novel network formation models with endogenous dynamical processes and strategic node-level decision-making, and characterization of the effects of latencies and critical feedbacks on emerging network structure; b) theoretical framework for control of network formation that will provide optimal interventions to the decision-making, the dynamic process or the network structure by an external agent in order to shape the arising network features; c) consistent network representations of surface morphology evolution during finishing processes, and automated local finishing processes that are efficient and guarantee desired surface properties. The key technical novelty in modeling of network formation processes is the introduction of latency effects of environmental dynamics and node behavior, which yields a rich set of dynamics, questioning the robustness of fundamental network formation models. We propose to leverage recent works on influence maximization and optimal control with Kullback-Leibler control costs to provide a control theoretic framework for efficiently obtaining desired network structures given the nonlinear dynamics of coevolving networks. Our validation effort promises to show how the proposed theoretical framework can be transformative in novel application areas, e.g., smart finishing of 3D printed components.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.