Sensitivity and Non-Normality in Network Control and Failure Propagation

Project: Research project

Description

The rise of network science over the past two decades has created the expectation that we will soon be able to systematically optimize and control the behavior of complex networks, and in turn address numerous outstanding problems—from cascade control to the development of self-healing networks. While progress has been made, in many systems our ability to control is still limited due to challenges imposed by the combination of high dimensionality, nonlinearity, and strict constraints on feasible interventions, which sets networks apart from other systems to which control has been traditionally applied. Prior progress on designing control methods scalable to large networks has been driven by the quest for new approaches, but none of these approaches takes explicit advantage of unique properties that emerge when networks are optimized for their function. An especially important such property is enhanced sensitivity to small perturbations, which has been seen as a source of instabilities and thus as yet another hurdle to control.

In this project, we will explore this enhanced sensitivity as an opportunity rather than an obstacle for controlling network systems. Of special interest to this research are (a) the recently established sensitive dependence of network dynamics on network structure and (b) the increasingly appreciated non-normality of many real network systems. These two properties can be shown to be prevalent in networks optimized to maximize a given objective function. Specifically, the project will (1) design a control approach based on sensitive dependence on network structure, (2) develop an optimization approach that avoids undesirable implications of non-normality, and (3) investigate how non-normality and sensitive dependence impact and can be controlled to mitigate the vulnerability to cascading failures in the U.S. power grid. The research will thus consist of mathematical and computational developments as well as applications. The expected outcomes include: (i) a scalable computational method to control complex networks, (ii) an optimization framework to enhance performance of complex networks without compromising their robustness, and (iii) the systematic study of cascading failures in the U.S. power grid, an important critical infrastructure to which results from (i) and (ii) will apply.

This research promises to strongly impact outstanding network problems of interest to the Army, including the control of cascading failures, the design of resilient networks responsive to interventions, and the identification of opportunities to promote robustly optimal operation of complex physical and socio-technological networks. Since a central thrust of the project is to explore how small local changes can induce global network response, the results are expected to be especially relevant to large-scale systems for which only local information is known in real time, and thus to a broad range of defense-related applications. The proposed application to the power grid addresses a well-recognized Army need for perturbation-tolerant infrastructure networks, and contributes to the development of self-healing smart network systems.

The project is inherently interdisciplinary and will involve collaborations between the PI (a physicist) and co-PI (a mathematician)—both with extensive expertise in network dynamics. The project will also involve a full-time postdoctoral researcher, to whom this research will provide a unique interdisciplinary training opportunity, thus contributing to the formation of the next generation of inter
StatusActive
Effective start/end date7/17/197/16/22

Funding

  • Army Research Office (W911NF1910383)

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Complex networks
Critical infrastructures
Computational methods
Large scale systems