MATH Seminar: “Consensus in networks of anticipatory agents under transmission delays”, Zeynep Güven, 1:00PM June 28 2024 (EN)

You are cordially invited to the M.S. Thesis Defense Presentation

“Consensus in networks of anticipatory agents under transmission delays”

Zeynep Güven, M.S. Student in Mathematics

Abstract: We investigate the linear consensus problem on undirected graphs consisting of anticipatory agents in the presence of an information transmission delay. The agents anticipate the states of their neighbours using past information through a first-order linear extrapolation, thereby introducing an additional delay into the dynamics and resulting in a coupled system of delay-differential equations with two discrete delays. We derive an exact condition for the system to achieve consensus from arbitrary initial conditions and demonstrate, through simulations, the positive impact of anticipation on the convergence rate of the consensus protocol under transmission delays.

Furthermore, we examine the Kuramoto model, a nonlinear synchronization model of coupled phase oscillators, where identical oscillators exhibit anticipatory behaviour in the presence of transmission delays. By applying our findings for the consensus problem to the linearized equation of the extended Kuramoto model, we derive an exact condition for the local stability of synchronized solutions, revealing that the delay margin is inversely proportional to the coupling strength between agents.

Advisor: Prof. Dr. Fatihcan Atay
Date: June 28, 2024
Time: 13:00
Place: SA – 141