Mean Field Estimation for Partially Observed LQG Systems with Major and Minor Agents

Abstract

In the work of Huang (2010) and Nguyen and Huang (2012) the linear quadratic mean field systems and control problem is solved in the case where there is a major agent (i.e. non-asymptotically vanishing as the population size goes to infinity) together with a population of minor agents (i.e. individually asymptotically negligible). The new feature in this case is that the mean field becomes stochastic and by minor agent state extension Nguyen and Huang (2012) establish the existence of e-Nash equilibria together with the individual agents' control laws that yield the equilibria. This paper presents results initially announced in Caines and Kizilkale (2013); Caines (2013) where it is shown that if the major agent's state is partially observed by the minor agents, and if the major agent completely observes its own state, all agents can recursively generate estimates (in general individually distinct) of the major agent's state and the mean field, and thence generate feedback controls yielding ∈-Nash equilibria.