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arXiv · 2404.12793

Transport maps as flows of control-affine systems

Marco Caponigro·Arianna Vicari
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Abstract

We consider the problem of transporting \nota{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.

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Marco Caponigro, Arianna Vicari. 2024-04-19. Transport maps as flows of control-affine systems. https://arxiv.org/abs/2404.12793

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