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

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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.