Optimal Control from a Fluid Dynamics Perspective

TL;DR

This paper presents a novel approach to solving optimal control problems, like Zermelo's problem, by reformulating them as multi-fluid dynamics problems, enabling large-scale and multi-agent navigation solutions using CFD tools.

Contribution

It introduces a fluid dynamics perspective to optimal control, allowing classical problems to be tackled with CFD methods and extended to larger, multi-agent scenarios.

Findings

Enables solving optimal navigation problems with CFD packages.

Allows large-area and multi-ship control in optimal navigation.

Draws parallels between fluid control and fluid animation techniques.

Abstract

An optimal control problem described by the Hamilton-Jacobi-Bellman equation can be developed into a problem that can be solved by general computational fluid dynamics packages. We describe how this formulation would allow a classical problem in optimal control, Zermelo's problem, to be treated as a multi-fluid problem. This approach has the advantage of allowing optimal navigation problems to be conducted over large areas, as well as to include moderately larger numbers of ships. We draw comparisons between this approach and the field of fluid control for fluid animations in movies.