  Feedback control synthesis for large-scale particle systems is reviewed in
the framework of model predictive control (MPC). The high-dimensional character
of collective dynamics hampers the performance of traditional MPC algorithms
based on fast online dynamic optimization at every time step. Two alternatives
to MPC are proposed. First, the use of supervised learning techniques for the
offline approximation of optimal feedback laws is discussed. Then, a procedure
based on sequential linearization of the dynamics based on macroscopic
quantities of the particle ensemble is reviewed. Both approaches circumvent the
online solution of optimal control problems enabling fast, real-time, feedback
synthesis for large-scale particle systems. Numerical experiments assess the
performance of the proposed algorithms.
