On the geometry of Zermelo’s optimal control trajectories
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 syste...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Amirkabir University of Technology
2022-02-01
|
| Series: | AUT Journal of Mathematics and Computing |
| Subjects: | |
| Online Access: | https://ajmc.aut.ac.ir/article_4542_e97d2e032d88876e90e0aeae3c9fc652.pdf |
| _version_ | 1797307118147076096 |
|---|---|
| author | Zohreh Fathi Behroz Bidabad |
| author_facet | Zohreh Fathi Behroz Bidabad |
| author_sort | Zohreh Fathi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T00:51:42Z |
| format | Article |
| id | doaj.art-2ca495a6487f463690f8ab1784a5a8f4 |
| institution | Directory Open Access Journal |
| issn | 2783-2449 2783-2287 |
| language | English |
| last_indexed | 2024-03-08T00:51:42Z |
| publishDate | 2022-02-01 |
| publisher | Amirkabir University of Technology |
| record_format | Article |
| series | AUT Journal of Mathematics and Computing |
| spelling | doaj.art-2ca495a6487f463690f8ab1784a5a8f42024-02-14T19:38:17ZengAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492783-22872022-02-013111010.22060/ajmc.2021.20459.10664542On the geometry of Zermelo’s optimal control trajectoriesZohreh Fathi0Behroz Bidabad1Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave. 15914 Tehran, IranFaculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave. 15914 Tehran, IranIn 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.https://ajmc.aut.ac.ir/article_4542_e97d2e032d88876e90e0aeae3c9fc652.pdfoptimal controlzermelo navigationfinslerranders metricgeodesic |
| spellingShingle | Zohreh Fathi Behroz Bidabad On the geometry of Zermelo’s optimal control trajectories AUT Journal of Mathematics and Computing optimal control zermelo navigation finsler randers metric geodesic |
| title | On the geometry of Zermelo’s optimal control trajectories |
| title_full | On the geometry of Zermelo’s optimal control trajectories |
| title_fullStr | On the geometry of Zermelo’s optimal control trajectories |
| title_full_unstemmed | On the geometry of Zermelo’s optimal control trajectories |
| title_short | On the geometry of Zermelo’s optimal control trajectories |
| title_sort | on the geometry of zermelo s optimal control trajectories |
| topic | optimal control zermelo navigation finsler randers metric geodesic |
| url | https://ajmc.aut.ac.ir/article_4542_e97d2e032d88876e90e0aeae3c9fc652.pdf |
| work_keys_str_mv | AT zohrehfathi onthegeometryofzermelosoptimalcontroltrajectories AT behrozbidabad onthegeometryofzermelosoptimalcontroltrajectories |