Estimation and Design of Uncertain Network Dynamics for Infrastructure-Management Applications

As modern infrastructure networks become increasingly stressed and multi-faceted, new research problems concerning their dynamics are arising. One keystone challenge is that infrastructure network operations are subject to internal and environmental uncertainties, both of which play a critical role in shaping the networks' dynamics and determining their performances. To meet this challenge, advanced modeling, estimation, and design tools are needed, that permit management of complex network dynamics under uncertainty. My research is concerned with developing estimation and control methods for networks subject to uncertainty, that exploit connections between the network's topology (i.e., graph structure) and its dynamics. The research effort also includes development of tools that are directly useful in infrastructural applications (including primarily air traffic management), in that they 1) permit prediction and characterization of dynamics; and 2) inform system management and decision-making processes at desired time/scale horizons.
In this seminar, two studies on estimation/design of uncertain network dynamics will be discussed: 1) a security and discoverability analysis for dynamical networks; and 2) a parameter-design study for a class of stochastic automata known as influence models. For the first topic, we first motivate and develop a broader definition of security/discoverability, as a measure of estimability of physical network dynamics and structure from noisy response measurements obtained by a cyber-adversary. We then present graph-theoretic characterizations of security for some canonical network models (including a network-spread model and a vehicle-team model), that draw on network state estimation concepts. For the second topic, we first show that influence models can be designed to generate sets of binary data with specified first- and second- moments. As a more sophisticated example, we also develop an influence-model-based weather-impact simulator for flow contingency management in air traffic systems, that is parameterized to statistically match probabilistic forecasts at snapshot times.

: Dr. Mengran Xue received a B.S. in Electrical Engineering from the University of Science and Technology of China and Ph.D. in Electrical Engineering from Washington State University, in 2007 and 2012 respectively. She currently works as a Postdoctoral Research Fellow with Prof. Ian A. Hiskens at the University of Michigan. Her research is focused on uncertainty modeling and evaluation in complex networks, with applications to power networks, aerospace systems, and others.