Minimax and Viscosity Solutions in Optimization Problems for Hereditary Systems / Lukoyanov N. Yu. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2010. - V. 269, l. 1. - P. S214-S225.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

For a dynamical system with discrete and distributed time delays, a control problem under disturbance or counteraction is considered. The problem is formalized in the context of the game-theoretical approach in the class of control strategies with memory. The problem is associated with a functional Hamilton-Jacobi type equation with coinvariant derivatives. The minimax and viscosity approaches to a generalized solution to this equation are discussed. It is shown that, under the same condition at the right endpoint, the minimax and viscosity solutions coincide, thereby uniquely defining the functional of optimal guaranteed result in the control problem.

Author keywords:

optimal control; differential games; time-delay systems; Hamilton-Jacobi equations; minimax solution; viscosity solution

DOI:

10.1134/S0081543810060179

Web of Science ID:

ISI:000209701100017

Соавторы в МНС:

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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	nyul@imm.uran.ru
ResearcherID-Numbers	Lukoyanov , Nikolai/Q-6872-2016
Funding-Acknowledgement	Presidium of the Russian Academy of Sciences ``Mathematical Control Theory{''}; Russian Foundation for Basic Research {[}09-01-00313]; Program for State Support of Leading Scientific Schools of Russia {[}NSh-2640.2008.1]
Funding-Text	This work was supported by the Program for Fundamental Research of the Presidium of the Russian Academy of Sciences ``Mathematical Control Theory,{''} by the Russian Foundation for Basic Research (project no. 09-01-00313), and by the Program for State Support of Leading Scientific Schools of Russia (project no. NSh-2640.2008.1).
Number-of-Cited-References	33
Usage-Count-Since-2013	3
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	V43SM