Mathematics and Statistics Colloquium

  • September 23, 2021
  • 4:30 PM - 5:30 CST
  • Cuneo Hall Room 311
  • Tuyen Tran, ttran18@luc.edu
  • Free
  • Not open to the public.
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  • Details

    Speaker: Rafal Goebel

    Title: The consensus and rendezvous problems

    Abstract: The consensus problem for a multi-agent system is about whether the agents (say, autonomous robots or individuals in a social network) can exchange information to reach a common opinion. A special case, known as the rendezvous problem, is about the agents asymptotically arriving at the same location. The challenges lie in the agents only being able to communicate their current opinion/location to their neighbors; in the communication structure changing over time; in constraints on the opinion/location of each agent; etc. The role of mathematics in this is, among other things, to prove that the given information structure and the chosen opinion adjustment/location control strategy works. Focusing on the rendezvous problem, the talk will show how elements of differential equations, linear algebra, graph theory, optimization, convex analysis, and switching dynamical system theory are involved in establishing convergence of the agents to the same location. The talk is based on joint work with Ricardo Sanfelice. 200-level calculus, differential equations, and linear algebra background should suffice for most of the talk.

    About the speaker: Professor Goebel joined the Department of Mathematics and Statistics at Loyola University Chicago in 2008. His interests include convex, nonsmooth, and set-valued analysis; control theory, including optimal control; hybrid dynamical systems; and optimization.