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

本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，其中时间延迟和相应的复杂行为起着重要作用。这种情况的一个例子是正在进行的COVID-19大流行，这些影响导致"反射”传播波，导致难以预测/控制感染传播的多个阶段。为了加强对大流行病的防范，并使医疗保健系统和政府做好准备，以最佳方式应对未来潜在的空气传播流行病，必须生成我们的互联社会和疾病传播的准确网络模型。使用这样的现实模型，最优控制策略可以综合考虑网络中的时间延迟所引起的复杂行为。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制定管理流行病局势的战略。 从外联到大学预科生到研究生培训，教育积极主动地纳入了这一项目的各个层面。扩大参与的战略将利用PI与机构资源和计划的联系，帮助从代表性不足的群体中招收学生。有效缓解通过网络传播的流行病需要：（a）从实验数据中揭示基础网络的拓扑结构、动态和延迟;（B）利用这一信息设计网络，使其能够有力地尽量减少局部感染病灶的系统影响，同时尊重总体最低限度的通信量限制;以及（c）合成调整局部参数的实时最优控制律，以防止大流行病传播的延迟引起的回声波的开始。本研究旨在实现这些目标，通过嵌入到一个更一般的问题：数据驱动的控制综合网络系统中存在的延迟引起的非最小相位/非被动行为，在场景中，系统的互连结构可能不是完全已知的先验。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，从而形成计算上易于处理的框架。拓扑识别将通过一个原子规范框架来完成。网络综合将联合收割机的想法，从网络控制和占领措施，设计和维持最佳的拓扑结构在一个缓慢的时间尺度。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性。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。

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.