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ISS Informal Systems Seminar

Linear Stochastic Graphon Systems with Q-Noise


Nov 10, 2023   10:30 AM — 11:30 AM

Alex Dunyak McGill University, Canada

Alex Dunyak

Presentation on YouTube.

Large networks are very common objects in engineering. One approach to modeling dynamical systems on large, dense networks is to use their associated graphon limit, which is a bounded function defined on the unit square [Lovasz, 2012]. In this talk, whose foundations were presented in [Dunyak, Caines, CDC 2022], we outline recent results extending classical stochastic linear systems theory to systems on very large graphs by utilizing their approximating graphons and Q-noise. This results in a stochastic differential equation in the space of square-integrable functions defined over the whole network. We demonstrate that a linear quadratic Gaussian (LQG) optimal control problem on a large network converges to a Q-noise LQG on a graphon. Then, when a graphon limit corresponds to a finite rank linear operator, the state of the system can be explicitly calculated. Finally, for a linear stochastic mean-field tracking game on a large graph, the Nash Equilibrium can be approximated by an optimal control problem on a graphon. The optimal inputs for each agent in the graphon can be solved for explicitly, giving a closed form solution.

Peter E. Caines organizer
Aditya Mahajan organizer
Shuang Gao organizer
Borna Sayedana organizer
Alex Dunyak organizer


Room MC 437
McConnell Building
McGill University
3480, rue University
Montréal QC H3A 0E9

Associated organization

Centre for intelligent machines (CIM)

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