Optimal Transport in Systems and Control
Optimal Transport in Systems and Control
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DOI：
10.1146/annurev-control-070220-100858
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发表时间：
2021-01-01
期刊：
影响因子：
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通讯作者：
Pavon, Michele
中科院分区：
文献类型：
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作者：
Chen, Yongxin;Georgiou, Tryphon T.;Pavon, Michele
最优运输最初是如何在生产者和消费者之间有效地重新分配商品的问题，并演变成一个影响深远的几何变分框架，用于研究度量空间上的分配流。该理论使得一类随机控制问题能够调节动力系统，从而将不确定性限制在指定的范围内。代表性的控制示例包括航天器按概率瞄准目标的着陆以及抑制热噪声对谐振器的不良影响；在这两个示例中，目标都是调节随机状态的分布流。概率分布传输与埃尔文·薛定谔提出的最大熵推理问题之间出现了最不可能的联系，后者被视为前者的熵正则化版本。最优传输、随机控制和推理这些相互交织的主题是本次综述的主题，旨在强调联系、见解和计算工具，同时涉及离散空间和网络中的二次调节器理论和概率流。
Optimal transport began as the problem of how to efficiently redistribute goods between production and consumers and evolved into a far-reaching geometric variational framework for studying flows of distributions on metric spaces. This theory enables a class of stochastic control problems to regulate dynamical systems so as to limit uncertainty to within specified limits. Representative control examples include the landing of a spacecraft aimed probabilistically toward a target and the suppression of undesirable effects of thermal noise on resonators; in both of these examples, the goal is to regulate the flow of the distribution of the random state. A most unlikely link turned up between transport of probability distributions and a maximum entropy inference problem posed by Erwin Schrodinger, where the latter is seen as an entropy-regularized version of the former. These intertwined topics of optimal transport, stochastic control, and inference are the subject of this review, which aims to highlight connections, insights, and computational tools while touching on quadratic regulator theory and probabilistic flows in discrete spaces and networks.