  In this paper, we study the optimal control system driven by stochastic
differential equations (SDEs) of mean-field type, in which the control variable
has two components, the first being absolutely continuous and the second
singular. On the other hand, the coefficients depend on the state of the
solution process as well as of its expected value. Moreover, the cost
functional is also of mean field type. This makes the control problem time
inconsistent in the sense that the Bellman optimality principle does not hold.
Our aim is to derive a stochastic maximum principle of optimal control of
Pontriagin type to the class of measure-valued controls.
