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Tue, December 15, 2015
The emergence of large networked systems has brought about new challenges to researchers and practitioners alike. While such systems perform well under normal operations, they can exhibit fragility in response to certain disruptions that may lead to catastrophic cascades of failures. This phenomenon, referred to as systemic risk, emphasizes the role of the system interconnection in causing such, possibly rare, events. The flash crash of 2010, the financial crisis of 2008, the New England power outage of 2003, or simply extensive delays in air travel, are just a few of many examples of fragility and systemic risk present in complex interconnected systems. Robust interconnections have been the subject of study by the control community for several decades. Substantial progress has been made in the context of both stability and performance robustness for various types of interconnections. Typical problems addressed in the literature involve interconnections with simple topologies, but with more complex components (dynamic, sometimes with high dimensions). More recently, the attention of the research community has shifted towards networked systems where the topology of the network is fairly large and complicated, while the local dynamics are fairly simple. The term fragility is used in this context to highlight the system's closeness to failure. Notions of failure include large amplification of local disturbances (or shocks), instability, or a substantial increase in the probability of extreme events. Cascaded failures, or systemic risk, fit under this umbrella and focus on local failures synchronizing to cause a breakdown in the network. Many abstracted models from transportation, finance, or the power grid fit this framework well. The focus of research is to relate fragility to the size and characteristics of a network for certain types of local interactions. In this talk, I will address this emerging area. I will provide some constructive examples and highlight important research directions.
