Seminar Scientific Computing (Prof. Marco Caponigro)

In this talk we consider the problem of transporting one probability measure into another through the flow of a driftless control-affine system.
Under suitable regularity conditions, controllability of the system by means of open-loop controls ensures the existence of time-varying feedback controls whose time-one flow realizes the optimal transport map for the quadratic cost.
The analysis connects the controllability of finite-dimensional systems with that of the associated continuity equation, providing a macroscopic description of evolving probability measures. These controllability problems arise naturally in the simultaneous control of large-scale multi-agent systems, where agent distributions evolve as controlled densities, or in Neural Ordinary Differential
Equations, where control inputs correspond to parameters in continuous-depth models.