Subspace Decompositions in Graphon Control and Graphon Mean Field Games

Virtual Informal Systems Seminar (VISS) Centre for Intelligent Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisions (GERAD)

Zoom Link
Meeting ID: 910 7928 6959 Passcode: VISS

Speaker: Shuang Gao, Postdoc Researcher, Electrical and Computer Engineering, McGill University

Abstract:
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).