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.

翻译：在模型预测控制（MPC）框架下，综述了大尺度粒子系统的反馈控制综合方法。集体动力学的高维特性阻碍了基于每个时间步快速在线动态优化的传统MPC算法的性能。本文提出两种MPC的替代方案：首先，讨论利用监督学习技术对最优反馈律进行离线近似的方法；其次，回顾基于粒子系综宏观量进行动力学序列线性化的流程。这两种方法均避免了在线求解最优控制问题，从而实现了大尺度粒子系统的快速实时反馈综合。数值实验评估了所提算法的性能。