Dynamical optimal transport of nonlinear control-affine systems
Karthik Elamvazhuthi,
Siting Liu,
Wuchen Li
et al.
Abstract:In this paper, we consider the fluid dynamical formulation of optimal transport for general nonlinear control systems that are of control-affine form for general cost functionals. When the system is driftless, this corresponds to the sub-Riemannian optimal transport problem. We first consider the issue of existence of solutions for this optimization problem. We introduce a relaxed formulation of the problem where the controls are allowed to be measure valued. Using this relaxed formulation, we provide a simple… Show more
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