Linear Stochastic Graphon Systems with Q-Noise
Informal Systems Seminar (ISS) Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)
Speaker: Alex Dunyak, PhD candidate in the department of electrical engineering at 平特五不中
**听狈辞迟别听迟丑补迟听迟丑颈蝉听颈蝉听补听丑测产谤颈诲听别惫别苍迟
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笔补蝉蝉肠辞诲别:听痴滨厂厂
Abstract: 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.
