  In this paper the optimal control of alignment models composed by a large
number of agents is investigated in presence of a selective action of a
controller, acting in order to enhance consensus. Two types of selective
controls have been presented: an homogeneous control filtered by a selective
function and a distributed control active only on a selective set. As a first
step toward a reduction of computational cost, we introduce a model predictive
control (MPC) approximation by deriving a numerical scheme with a feedback
selective constrained dynamics. Next, in order to cope with the numerical
solution of a large number of interacting agents, we derive the mean-field
limit of the feedback selective constrained dynamics, which eventually will be
solved numerically by means of a stochastic algorithm, able to simulate
efficiently the selective constrained dynamics. Finally, several numerical
simulations are reported to show the efficiency of the proposed techniques.
