Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance
Abstract
It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational obstacle-avoidance formulation for incompressible ideal flows by introducing a barrier-type potential in the associated optimal control functional. This leads to \textit{modified Euler equations for an inviscid fluid}, in which the barrier term acts on the Lagrangian configuration and appears in the Eulerian description as a shift in the effective pressure. We also present a numerical illustration of the reduced Eulerian dynamics, showing that the barrier term induces a localized deformation of the flow near the obstacle region, consistent with its role as an obstacle-avoidance penalization.
Cite
@article{arxiv.2311.01774,
title = {Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance},
author = {Alexandre Anahory Simoes and Anthony Bloch and Leonardo Colombo},
journal= {arXiv preprint arXiv:2311.01774},
year = {2026}
}
Comments
6 pages, conference