Collaborative Research: Modeling and Control of Non-Passive Networks with Distributed Time-Delays: Application in Epidemic Control

这项研究旨在为大规模网络的数据驱动控制开发一个全面的框架，在大规模网络中，时延和相应的复杂行为发挥着重要作用。这种情况的一个例子是正在进行的新冠肺炎大流行，这些影响导致“反射性”传播波，导致难以预测/控制感染传播的多个阶段。为了加强对大流行的准备，并使医疗保健系统和政府做好以最佳方式应对未来潜在的空气传播流行病的准备，必须生成我们相互关联的社会和疾病传播的准确网络模型。使用这样的现实模型，可以综合考虑网络中时滞引起的复杂行为的最优控制策略。该项目将解决这一未得到满足的需求，这将产生重大的社会影响，并可帮助利益攸关方设计战略来管理大流行局势。从推广到大学预科学生到研究生培训，所有各级的教育都积极纳入这一项目。扩大参与的战略将利用私人投资机构与机构资源和项目的联系，帮助从代表性不足的群体中招收学生。有效缓解流行病在网络上传播需要：(A)根据实验数据揭示底层网络的拓扑、动态和延迟；(B)利用这些信息设计网络，使局部感染中心的系统性影响降至最低，同时尊重总体最低限度的交通限制；(C)合成实时最优控制律，调整局部参数，以防止因延迟引起的大流行传播的回声波的开始。该研究试图通过将问题嵌入到一个更一般的问题中来实现这些目标：在系统的互连结构可能不是完全先验已知的情况下，存在延迟诱导的非最小相位/非被动行为的网络系统的数据驱动控制综合。这种嵌入允许利用丰富的知识库，从非线性识别和半代数优化到基于无源性的网络控制，导致了一个计算上易于处理的框架。拓扑识别将通过原子规范框架完成。网络综合将结合网络控制和占用措施的思想，在较慢的时间尺度上设计和维护最优拓扑。实时最优控制律将使用事件触发的钝化来防止延迟引起的不稳定。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research seeks to develop a comprehensive framework for data-driven control of large-scale networks where time delays and the corresponding complex behavior play a substantial role. An example of this situation is the ongoing COVID-19 pandemic, where these effects lead to ``reflective" spreading waves, resulting in hard to predict/control multiple phases of infection spread. To enhance pandemic preparedness and make healthcare systems and governments ready to optimally respond to potential future airborne epidemic disease, it is imperative to generate accurate network models of our connected society and disease spread. Using such realistic models, optimal control strategies can be synthesized that take into account the complex behavior caused by time delays in the network. This project will address this unmet need, which will have a significant social impact and can help stakeholders design strategies to manage a pandemic situation. Education is proactively integrated into this project at all levels, from outreach to pre-college students to graduate training. The strategy to broaden participation will leverage PIs’ connections to institutional resources and programs to help recruit students from underrepresented groups. Effective mitigation of pandemics spreading over networks requires: (a) unveiling the topology, dynamics and delays of the underlying network from experimental data; (b) use of this information to design networks that can robustly minimize the systemic effects of localized infection foci, while respecting overall minimum traffic constraints; and (c) synthesizing real-time optimal control laws that adjust local parameters to prevent the onset of delay-induced echoing waves of pandemic spread. This research seeks to achieve these objectives by embedding the problem into a more general one: data-driven control synthesis for networked systems in the presence of delay-induced non-minimum phase/non-passive behavior, in scenarios where the interconnection structure of the system may not be perfectly known a priori. This embedding allows for exploiting a rich knowledge base, ranging from non-linear identification and semi-algebraic optimization to passivity-based control of networks, leading to a computationally tractable framework. Topology identification will be accomplished through an atomic norm framework. Network synthesis will combine ideas from network control and occupation measures to design and maintain optimal topologies at a slow time scale. Real-time optimal control laws will use event-triggered passivation to prevent delay-induced instabilities.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.