Asymptotics of the Optimal Time in a Time-Optimal Control Problem with a Small Parameter / Danilin A. R.,Kovrizhnykh O. O. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2017. - V. 297, l. 1. - P. S62-S71.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

A time-optimal control problem for a singularly perturbed linear autonomous system is considered. The main difference between this case and the case of systems with fast and slow variables studied earlier is that the eigenvalues of the matrix at the fast variables do not satisfy the standard requirement of negativity of the real part. We obtain and justify a complete power asymptotic expansion in the sense of Erdelyi of the optimal time and optimal control in a small parameter at the derivatives in the equations of the system.

Author keywords:

optimal control; time-optimal control problem; asymptotic expansion; singularly perturbed problems; small parameter

DOI:

10.1134/S0081543817050078

Web of Science ID:

ISI:000410252500007

Соавторы в МНС:

—

Другие поля

Поле	Значение
Month	JUL
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]; Russian Academic Excellence Project {[}02.A03.21.0006]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project no. 14-01-00322) and by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
Number-of-Cited-References	16
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	1
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	FG4RG