A Boltzmann approach to mean-field sparse feedback control

We study the synthesis of optimal control policies for large-scalemulti-agent systems. The optimal control design induces a parsimonious controlintervention by means of l-1, sparsity-promoting control penalizations. Westudy instantaneous and infinite horizon sparse optimal feedback controllers.In order to circumvent the dimensionality issues associated to the control oflarge-scale agent-based models, we follow a Boltzmann approach. We generate(sub)optimal controls signals for the kinetic limit of the multi-agentdynamics, by sampling of the optimal solution of the associated two-agentdynamics. Numerical experiments assess the performance of the proposed sparsedesign.