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.

大规模粒子系统的反馈控制合成在模型预测控制（MPC）框架内进行回顾。集体动力学的高维特性阻碍了传统MPC算法的性能，该算法基于每个时间步的快速在线动态优化。提出了两种MPC的替代方案。首先，讨论了使用监督学习技术对最优反馈定律进行离线近似的方法。然后，回顾了一种基于粒子集合宏观量的顺序线性化动态的过程。这两种方法绕过了在线求解最优控制问题，实现了大规模粒子系统的快速实时反馈合成。数值实验证明了所提出算法的性能。

基于数据/时刻驱动的集体动力学快速预测控制方法