Weakly coupled systems of eikonal equations for autonomous vehicles
Optimization and Control
2024-05-22 v2
Abstract
In this paper, we study solutions for a weakly coupled system of eikonal equations arising in an optimal path-planning problem with random breakdown. The model considered takes into account two types of breakdown for the vehicle, partial and total, which happen at a known, spatially inhomogeneous rate. In particular, we analyze the complications due to the delicate degenerate coupling condition by using existing results on weakly coupled systems of Hamilton-Jacobi equations. Then we consider finite element method schemes built for convection-diffusion problems to construct approximate solutions for this system and produce some numerical simulations.
Cite
@article{arxiv.2310.02966,
title = {Weakly coupled systems of eikonal equations for autonomous vehicles},
author = {Maria Teresa Chiri and Kenneth D Czuprynski and Ludmil T Zikatanov},
journal= {arXiv preprint arXiv:2310.02966},
year = {2024}
}
Comments
6 pages, two columns