(5/10/2016, Communications in Industrial and Applied Mathematics, 9(2):4-21, 2018, arxiv: 1603.05012)
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 the control. 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 introduce a binary interaction algorithm which is able to simulate efficiently the selective constrained dynamics. Consistency of the algorithm is also shown in the context of standard kinetic theory. Finally, some numerical simulations are reported to show the efficiency of the proposed techniques.