Groupe d’études et de recherche en analyse des décisions

Subspace decompositions in graphon control and graphon mean field games

Shuang Gao Département de génie électrique et informatique, Université McGill, Canada

Shuang Gao

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Nº du webinaire : 910 7928 6959
Code secret: VISS

Graphon control (CDC 17-18-19, IEEE TAC 20, Gao and Caines) and graphon mean field games (CDC18, CDC19, Caines and Huang) were used to address decision problems on very large-scale networks by employing graphons to represent arbitrary size graphs, from, respectively centralized and decentralized perspectives. Graphon couplings may appear in states, controls and cost, and may be represented by different graphons in each case. In this talk, I will first briefly introduce graphon theory. Then I will present the use of subspace decompositions in graphon control and graphon mean field games in a linear quadratic setting. The complexity of the methods corresponds to that of the solution of one nd × nd dimensional Riccati equation and one n × n Riccati equation, where n is the dimension of each nodal agent state and d is the dimension of the (nontrivial) invariant subspace shared by the coupling operators. Applications to the regulation of harmonic oscillators coupled over networks with uncertainties will be demonstrated (IEEE TCNS (Submitted), Gao and Caines).