TY - GEN
T1 - Weakly Coupled Systems of Eikonal Equations in Path-Planning Problems
AU - Chiri, Maria Teresa
AU - Czuprynski, Kenneth D.
AU - Zikatanov, Ludmil Tomov
N1 - Publisher Copyright:
© 2024 AACC.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
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U2 - 10.23919/ACC60939.2024.10644838
DO - 10.23919/ACC60939.2024.10644838
M3 - Conference contribution
AN - SCOPUS:85204447747
T3 - Proceedings of the American Control Conference
SP - 5036
EP - 5041
BT - 2024 American Control Conference, ACC 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 American Control Conference, ACC 2024
Y2 - 10 July 2024 through 12 July 2024
ER -