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Special Seminar: From Simple Graph Measures to Complex System Properties: How Distances and Degrees Affect the Controllability and Robustness of Networks?

Yasin Yazicioglu

2:30 PM on 2019-03-12

3-180 Keller Hall


Diffusively coupled networks appear in a wide range of natural and engineered systems. In such networks, each node has a state that is attracted towards some weighted average of the states of its neighbors. While this type of local averaging can be used to model naturally occurring phenomena like diffusion of a substance, spread of opinions in societal networks, or synchronization of coupled oscillators; it can also be used in designing coordination algorithms for distributed systems (e.g., for achieving rendezvous or formation flight by a team of robots). In diffusively coupled networks, properties like stability, convergence rate, controllability, or robustness significantly depend on the interaction graph.

In this talk, I will present some fundamental connections between the controllability and robustness of diffusively coupled networks and the structure of their interaction graphs. In particular, I will show that two simple graph measures, namely the degrees (the number of links each node has) and the distances (the lengths of the shortest paths between the nodes), imply tight upper and lower bounds on the network’s structural controllability and robustness. This structural analysis is based on the worst/best-case values of these properties under admissible coupling weights. In this context, the controllability is quantified through the smallest (worst) possible dimension of the controllable subspace when external control inputs are injected to some specific nodes, and robustness is quantified through the smallest (best) possible value of the expected steady state variance of states under white Gaussian noise. The proposed bounds are particularly useful for the analysis, design, and control of large-scale networks since the distances and degrees can be easily computed for networks of any size. Accordingly, they can be used for tasks like choosing a small number of control nodes that ensure controllability, designing robust networks, or analyzing how these system properties change with increasing size for a given network topology. I will demonstrate the use of these results through some applications in distributed robotics and conclude with some future directions in this domain.

BIO:

Yasin Yazıcıoğlu received the Ph.D. degree in Electrical and Computer Engineering from the Georgia Institute of Technology in 2014, and the B.S. and M.S. degrees in Mechatronics Engineering from Sabancı University, Turkey, in 2007 and 2009 respectively. After the completion of his Ph.D., he joined the Laboratory for Information and Decision Systems (LIDS) at MIT as a postdoctoral research associate. Since March 2018, he has been a research assistant professor in the Department of Electrical and Computer Engineering at the University of Minnesota. His research has been primarily focused on distributed decision making and control, with applications to cyber-physical and societal networks, and multi-robot systems.


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