Graphon spectral decompositions for LQG control and games

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 be considered as a generalization of mean-field couplings with network heterogeneity. Such couplings may appear in states, controls and cost, and may be represented by different graphons in each case. In this talk, I will present the use of graphon spectral decomposition in graphon control and graphon mean field games in a linear quadratic setting. The complexity of the method does not directly depend on the number of agents or number of nodes, instead, it depends on the dimension of the characterizing graphon invariant subspace shared by the coupling operators.