Asymptotics of the Optimal Time in a Time-Optimal Problem with Two Small Parameters / Danilin A. R.,Kovrizhnykh O. O. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 288, l. 1. - P. S46-S53.

ISSN/EISSN:
0081-5438 / 1531-8605
Type:
Article
Abstract:
A time-optimal problem of control of a small-mass point by a force of bounded magnitude in an unresisting medium is considered. An asymptotic expansion of the optimal time and optimal control is constructed with respect to two independent small parameters: the mass of the point and the perturbation of the initial conditions. It is shown that the asymptotics of the optimal time in this problem is complicated even for cases of general position.
Author keywords:
optimal control; time-optimal control problem; asymptotic expansion; singular perturbation problems; small parameter
DOI:
10.1134/S0081543815020066
Web of Science ID:
ISI:000352991400005
Соавторы в МНС:
Другие поля
Поле Значение
Month APR
Publisher MAIK NAUKA/INTERPERIODICA/SPRINGER
Address 233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language English
EISSN 1531-8605
Research-Areas Mathematics
Web-of-Science-Categories Mathematics, Applied; Mathematics
Author-Email dar@imm.uran.ru koo@imm.uran.ru
ORCID-Numbers Danilin, Aleksei Rufimovich/0000-0002-8711-2026
Funding-Acknowledgement Russian Foundation for Basic Research {[}14-01-00322]; Program for Fundamental Research of the Presidium of the Russian Academy of Sciences ``Fundamental Problems of Nonlinear Dynamics in Mathematics and Physics{''}; Ural Branch of the Russian Academy of Sciences {[}12-P-1-1009]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]
Funding-Text This work was partially supported by the Russian Foundation for Basic Research (project no. 14-01-00322), by the Program for Fundamental Research of the Presidium of the Russian Academy of Sciences ``Fundamental Problems of Nonlinear Dynamics in Mathematics and Physics{''} (with financial support of the Ural Branch of the Russian Academy of Sciences, project no. 12-P-1-1009), and by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013).
Number-of-Cited-References 15
Usage-Count-Last-180-days 1
Usage-Count-Since-2013 3
Journal-ISO Proc. Steklov Inst. Math.
Doc-Delivery-Number CG0VY