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UID:20260831T103635EDT-6392H5ubHU@132.216.98.100
DTSTAMP:20260831T143635Z
DESCRIPTION:Informal Systems Seminar (ISS) Centre for Intelligent Machines 
 (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)
 \n\nSpeaker: Alex Dunyak\, PhD candidate in the department of electrical e
 ngineering at McGill University\n	\n	** Note that this is a hybrid event\n	\n
 	Zoom Link\n	Meeting ID: 845 1388 1004\n	Passcode: VISS\n	\n	\n	Abstract: Large 
 networks are very common objects in engineering. One approach to modeling 
 dynamical systems on large\, dense networks is to use their associated gra
 phon limit\, which is a bounded function defined on the unit square [Lovas
 z\, 2012]. In this talk\, whose foundations were presented in [Dunyak\, Ca
 ines\, CDC 2022]\, we outline recent results extending classical stochasti
 c linear systems theory to systems on very large graphs by utilizing their
  approximating graphons and Q-noise. This results in a stochastic differen
 tial equation in the space of square-integrable functions defined over the
  whole network. We demonstrate that a linear quadratic Gaussian (LQG) opti
 mal control problem on a large network converges to a Q-noise LQG on a gra
 phon. Then\, when a graphon limit corresponds to a finite rank linear oper
 ator\, 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 expli
 citly\, giving a closed form solution.\n
DTSTART:20231110T153000Z
DTEND:20231110T163000Z
LOCATION:Zames Seminar Room\, MC 437\, McConnell Engineering Building\, CA\
 , QC\, Montreal\, H3A 0E9\, 3480 rue University
SUMMARY:Linear Stochastic Graphon Systems with Q-Noise
URL:https://www.mcgill.ca/cim/channels/event/linear-stochastic-graphon-syst
 ems-q-noise-352582
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