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

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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.