  We study the optimal control of discrete time mean filed dynamical systems
under partial observations. We express the global law of the filtered process
as a controlled system with its own dynamics. Following a dynamic programming
approach, we prove a verification result providing a solution to the optimal
control of the filtered system. As an application, we study a general linear
quadratic example for which an explicit solution is given. We also describe an
algorithm for the numerical approximation of the optimal value and provide
numerical experiments on a financial example.
