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<p>We consider the problem of transporting one probability measure into another through the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop controls is a sufficient condition for the existence of time-varying feedback controls such that the 1-time flow of the system is the optimal transport map for the quadratic cost.</p>

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Transport Maps as Flows of Control-affine Systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月28日

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  • Marco Caponigro,
  • Arianna Vicari

摘要

We consider the problem of transporting one probability measure into another through the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop controls is a sufficient condition for the existence of time-varying feedback controls such that the 1-time flow of the system is the optimal transport map for the quadratic cost.