Graphon Control and Graphon Mean Field Games for General and LQG Systems
Abstract
Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently enabled the formulation of a Graphon Control (GC) theory of the centralized control of dynamical systems distributed on asymptotically infinite networks [Gao and Caines, IEEE CDC 2017, 2018]. Furthermore, the study of the decentralized control of such systems has also recently been initiated in [Caines and Huang, IEEE CDC 2018] where Graphon Mean Field Games (GMFG) are formulated for the analysis of non-cooperative dynamical games on unbounded networks. In this talk the GC and GMFG frameworks will first be presented, followed by the basic existence and uniqueness results for the GMFG equations, and an epsilon-Nash theorem relating the infinite population equilibria on infinite networks to that of finite population equilibria on finite networks. Finally, the special case of Linear Quadratic Gaussian (LQG) GMFG systems will be sketched for some simple graphons.
Work with Minyi Huang and Shuang Gao