Decentralized estimation in a class of measurements induced mean field control problems

We study a class of mean field control problems for a large population of linear Gaussian quadratic agents, coupled via their partial observations. The measurements interference model is assumed to depend only on the empirical mean of agents states. In addition, a structural assumption is made on the agents´ controls which are constrained to be linear constant feedbacks on a locally based state estimate. We investigate the ability of such a constrained structure to stabilize individual agent systems as the number of agents increases to infinity. Previous work has shown that a naive approach, whereby the coupling interference term is considered deterministic in the limit as is usually assumed in mean field approaches, results in poor local estimation results and consequently severely limits the stabilization abilities of the closed loop structure. Instead, the finite population optimal decentralized estimation problem is studied, and a non-recursive optimal estimation scheme is presented and tested numerically. This scheme can become a solid basis for deriving asymptotic local state estimate approximations.