Speaker: Dr. Amir Aghdam, Concordia University
Host: Professor Bahram Shafai
In this presentation, connectivity of an asymmetric network represented by a weighted directed graph is investigated. The notion of weighted vertex connectivity is introduced as a metric to evaluate the connectivity of a random sensor network where the elements of the weight matrix characterize the operational probability of their corresponding communication links. The weighted vertex connectivity measure extends the notion of vertex connectivity to weighted graphs by taking into account the joint effects of path reliability and network robustness to node failure. The problem of finding the weighted vertex connectivity measure is transformed into a sequence of iterative deepening depth-first search and maximum weight clique problems, and based on that, an algorithm is developed to find the proposed connectivity metric. The approximate weighted vertex connectivity measure is defined subsequently as a lower bound on the introduced connectivity metric which can be found by applying a series of a polynomial-time shortest path algorithm. The notion of generalized algebraic connectivity is also introduced as an extension of the algebraic connectivity to weighted directed graphs. This measure reflects the expected asymptotic convergence rate of cooperative algorithms used to control the network. This connectivity measure is then described in terms of the eigenvalues of the Laplacian matrix of the digraph representing the network. The advantage of this new metric over the algebraic connectivity measure in describing the connectivity of asymmetric networks is demonstrated using some counterintuitive examples. The generalized power iteration algorithm is then developed to compute the proposed connectivity measure in a distributed fashion. The performance of the proposed algorithm is validated using an experimental underwater acoustic sensor network.
Amir G. Aghdam received his Ph.D. in electrical and computer engineering from the University of Toronto in 2000 and is currently a Professor in the Department of Electrical and Computer Engineering at Concordia University. Dr. Aghdam is a member of the Conference Editorial Board of IEEE Control Systems Society, Co-Editor-in-Chief of the IEEE Systems Journal, an Associate Editor of the IEEE Transactions on Control Systems Technology, European Journal of Control, IET Control Theory & Applications, and Canadian Journal of Electrical and Computer Engineering.
He has been a member of the Technical Program Committee of a number of conferences including IEEE Conference on Systems, Man and Cybernetics, IEEE Conference on Decision and Control, and IEEE Multiconference on Systems and Control. Since August 2013, he has been a member of Natural Science and Engineering Research Council of Canada (NSERC) ECE Evaluation Group. Dr. Aghdam is 2014-2015 President of IEEE Canada and Director of IEEE Inc. (Region 7), and is also a member of IEEE Awards Board for this period. His research interests include multi-agent networks, distributed control, optimization and sampled-data systems.