论文标题
动力学共识控制的监督学习
Supervised learning for kinetic consensus control
论文作者
论文摘要
在本文中，讨论了如何成功有效地调节目标代理人达成共识的目标人群。为了克服维度的诅咒，考虑了共识控制问题的平均场公式。尽管这种公式的设计目的是独立于代理的数量，但仅求解代理空间的中等内在维度是可行的。因此，通过Boltzmann程序，即受控二进制相互作用的准不变极限作为平均场PDE的近似。对二进制交互控制问题有效的求解器的需求激发了使用监督的学习方法来编码以非常高的速度进行采样的二进制反馈图。考虑了用于二进制控制问题价值功能的梯度增强前馈神经网络，并将其与反馈定律的直接近似进行了比较。
In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse of dimensionality, the mean field formulation of the consensus control problem is considered. Although such formulation is designed to be independent of the number of agents, it is feasible to solve only for moderate intrinsic dimensions of the agents space. For this reason, the solution is approached by means of a Boltzmann procedure, i.e. quasi-invariant limit of controlled binary interactions as approximation of the mean field PDE. The need for an efficient solver for the binary interaction control problem motivates the use of a supervised learning approach to encode a binary feedback map to be sampled at a very high rate. A gradient augmented feedforward neural network for the Value function of the binary control problem is considered and compared with direct approximation of the feedback law.
