Linear Stochastic Graphon Systems with Q-Noise

Explore the cutting-edge research on modeling dynamical systems on large, dense networks using graphon limits in this 53-minute seminar presented by Alex Dunyak from McGill University. Delve into the extension of classical stochastic linear systems theory to systems on very large graphs, utilizing approximating graphons and Q-noise. Discover how this approach results in a stochastic differential equation in the space of square-integrable functions defined over the entire network. Learn about the convergence of linear quadratic Gaussian (LQG) optimal control problems on large networks to Q-noise LQG on graphons. Examine the explicit calculation of system states when graphon limits correspond to finite rank linear operators. Explore the approximation of Nash Equilibrium for linear stochastic mean-field tracking games on large graphs using optimal control problems on graphons, and understand how to derive closed-form solutions for optimal inputs for each agent in the graphon.