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LANS Seminar
April 26, 2023 @ 10:30 - 11:30 CDT
Seminar Title: Weak and Semi-Contraction for Large-Scale Network Systems
Speaker: Saber Jafarpour, Postdoctoral Research Fellow, Georgia Institute of Technology
Date/Time: April 26, 2023 / 10:30 AM – 11:30 AM
Location: See meeting URL on the cels-seminars website (requires Argonne login)
Host: Adrian Maldonado
Description: Dynamical systems on large-scale networks appear in numerous real-world applications, including traffic and power infrastructures, social interactions, chemical and biological systems, and neural networks. In most of these applications, dynamic networks feature large numbers of components and complicated patterns of interaction. Contraction theory is a scalable stability framework that defines stability incrementally between two arbitrary trajectories. However, the applicability of classical contraction theory to real-world networks is limited as these networks are often not strictly contracting due to conservation laws or symmetries. In this talk, we develop two extensions of contraction theory, namely weak contraction and semi-contraction. For weak-contracting systems, we provide a dichotomy for the asymptotic behavior of their trajectories and propose sufficient conditions for their convergence to equilibria. For semi-contracting systems, we study the convergence of their trajectories to affine invariant subspaces. Finally, we apply our results to two essential classes of network systems: i) continuous-time distributed primal-dual algorithms over networks and ii) diffusively coupled dynamical systems.
Bio: Saber Jafarpour is a postdoctoral research fellow in the Department of Electrical and Computer Engineering at the Georgia Institute of Technology. Before that, he was a postdoctoral researcher in the Center for Control, Dynamical Systems, and Computation at UC Santa Barbara. He received his Ph.D. in Mathematics and Statistics from Queen’s University in 2016. His research interests are centered around control theory and autonomy with applications to learning-based control systems and large-scale networks such as power grids and transportation networks.
Please note that the meeting URL for this event can be seen on the cels-seminars website, which requires an Argonne login.