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.
Caponigro, M., Vicari, A. (2025). Transport Maps as Flows of Control-affine Systems. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 31(3) [10.1007/s10883-025-09745-0].
Transport Maps as Flows of Control-affine Systems
Caponigro, Marco
;Vicari, Arianna
2025-01-01
Abstract
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.File in questo prodotto:
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