TY - JOUR
ID - 4542
TI - On the geometry of Zermelo's optimal control trajectories
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Fathi, Zohreh
AU - Bidabad, Behroz
AD - Faculty of Mathematics Amirkabir University of Technology
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Y1 - 2022
PY - 2022
VL - 3
IS - 1
SP - 1
EP - 10
KW - Optimal control
KW - Zermelo navigation
KW - Finsler
KW - Randers Metric
KW - Geodesic
DO - 10.22060/ajmc.2021.20459.1066
N2 - In the present work, we study the optimal control paths in the Zermelo navigation problem from the geometric and differential equations point of view rather than the optimal control point of view, where the latter has been carried out in our recent work. Here, we obtain the precise form of the system of ODE where the solutions are optimal trajectories of Zermelo's navigation problem.Having a precise equation allows optimizing a cost function more accurately and efficiently.The advantage of these equations is to approximate optimal trajectories in the general case by the first order approximation of external fields $w$. The latter could be solved numerically since we have retrieved simpler equations for these paths.
UR - https://ajmc.aut.ac.ir/article_4542.html
L1 - https://ajmc.aut.ac.ir/article_4542_9c3b0722a6e3294b44ca6b90179f05a7.pdf
ER -