پیوندهای مفید
آمار
| تعداد نشریات | 9 |
| تعداد شمارهها | 447 |
| تعداد مقالات | 5,734 |
| تعداد مشاهده مقاله | 8,047,193 |
| تعداد دریافت فایل اصل مقاله | 6,547,389 |
On the geometry of Zermelo’s optimal control trajectories | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 1، دوره 3، شماره 1، اردیبهشت 2022، صفحه 1-10 اصل مقاله (322.41 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20459.1066 | ||
| نویسندگان | ||
| Zohreh Fathi1؛ Behroz Bidabad* 1، 2 | ||
| 1Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave. 15914 Tehran, Iran | ||
| 2Institut de Math´ematique de Toulouse, Universit´e Paul Sabatier, F-31062 Toulouse, France | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Optimal control؛ Zermelo navigation؛ Finsler؛ Randers metric؛ Geodesic | ||
| مراجع | ||
|
[1] E. Bakolas and P. Tsiotras, Time-optimal synthesis for the Zermelo-markov-dubins problem: the constant wind case, in Proceedings of the 2010 American Control Conference, IEEE, 2010, pp. 6163–6168.
[2] D. Bao, S.-S. Chern, and Z. Shen, An introduction to Riemann-Finsler geometry, vol. 200, Springer Science & Business Media, 2012.
[3] D. Bao, C. Robles, and Z. Shen, Zermelo navigation on riemannian manifolds, Journal of Differential Geometry, 66 (2004), pp. 377–435.
[4] B. Bidabad and M. Rafie-Rad, Pure pursuit navigation on riemannian manifolds, Nonlinear Analysis: Real World Applications, 10 (2009), pp. 1265–1269.
[5] A. Enes and W. Book, Blended shared control of Zermelo’s navigation problem, in Proceedings of the 2010 American Control Conference, IEEE, 2010, pp. 4307–4312.
[6] Z. Fathi and B. Bidabad, Time-optimal solutions of Zermelo’s navigation problem with obstacles, Submitted.
[7] Z. Fathi, B. Bidabad, and M. Najafpour, An exact penalty function method for optimal control of a dubins airplane in the presence of moving obstacles, Optimization letters, (2021), pp. 1–17.
[8] M. R. Jardin and A. E. Bryson Jr, Methods for computing minimum-time paths in strong winds, Journal of Guidance, Control, and Dynamics, 35 (2012), pp. 165–171.
[9] C. Jiang, Q. Lin, C. Yu, K. L. Teo, and G.-R. Duan, An exact penalty method for free terminal time optimal control problem with continuous inequality constraints, Journal of Optimization Theory and Applications, 154 (2012), pp. 30–53.
[10] B. Li, K. L. Teo, C.-C. Lim, and G. R. Duan, An optimal pid controller design for nonlinear constrained optimal control problems, Discrete & Continuous Dynamical Systems-B, 16 (2011), p. 1101.
[11] B. Li, K. L. Teo, G. Zhao, and G. Duan, An efficient computational approach to a class of minmax optimal control problems with applications, The ANZIAM Journal, 51 (2009), pp. 162–177.
[12] B. Li, C. Xu, K. L. Teo, and J. Chu, Time optimal Zermelo’s navigation problem with moving and fixed obstacles, Applied Mathematics and Computation, 224 (2013), pp. 866–875.
[13] A. Marchidan and E. Bakolas, Numerical techniques for minimum-time routing on sphere with realistic winds, Journal of Guidance, Control, and Dynamics, 39 (2016), pp. 188–193.
[14] C. Robles, Geodesics in randers spaces of constant curvature, Transactions of the American mathematical society, (2007), pp. 1633–1651.
[15] Z. Shen, Finsler metrics with k= 0 and s= 0, Canadian Journal of Mathematics, 55 (2003), pp. 112–132. | ||
|
آمار تعداد مشاهده مقاله: 1,620 تعداد دریافت فایل اصل مقاله: 1,194 |
||