Selective model-predictive control for flocking systems

In this paper the optimal control of alignment models composed by a largenumber of agents is investigated in presence of a selective action of acontroller, acting in order to enhance consensus. Two types of selectivecontrols have been presented: an homogeneous control filtered by a selectivefunction and a distributed control active only on a selective set. As a firststep toward a reduction of computational cost, we introduce a model predictivecontrol (MPC) approximation by deriving a numerical scheme with a feedbackselective constrained dynamics. Next, in order to cope with the numericalsolution of a large number of interacting agents, we derive the mean-fieldlimit of the feedback selective constrained dynamics, which eventually will besolved numerically by means of a stochastic algorithm, able to simulateefficiently the selective constrained dynamics. Finally, several numericalsimulations are reported to show the efficiency of the proposed techniques.