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Séminaire informel de théorie des systèmes (ISS)

Linear Stochastic Graphon Systems with Q-Noise


10 nov. 2023   10h30 — 11h30

Alex Dunyak Université McGill, Canada

Alex Dunyak

Présentation sur 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 responsable
Aditya Mahajan responsable
Shuang Gao responsable
Borna Sayedana responsable
Alex Dunyak responsable


Salle MC 437
Pavillon McConnell
Université McGill
3480, rue University
Montréal QC H3A 0E9

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Centre for intelligent machines (CIM)

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