Optimal Transport in Systems and Control

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon

Research output: Contribution to journalReview articlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)89-113
Number of pages25
JournalAnnual Review of Control, Robotics, and Autonomous Systems
StatePublished - May 3 2021


  • covariance control
  • Markov decision processes
  • optimal transport
  • Schrödinger bridge
  • stochastic control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Engineering (miscellaneous)
  • Human-Computer Interaction
  • Artificial Intelligence


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