On the numerical solution of a minimax control problem with a positional functional / Gomoyunov M. I.,Kornev D. V.,Lukoyanov N. Yu. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 291, l. 1. - P. S77-S95.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

We consider a minimax feedback control problem for a linear dynamic system with a positional quality index, which is the norm of the set of deviations of the motion from given target points at given times. The problem is formalized as a positional differential game. A numerical method is given for finding an approximation of the game value and constructing an optimal (minimax and maximin) control law. The method is based on the recursive construction of upper convex (concave) hulls of auxiliary program functions. In addition, we use the ``pixel{''} approximation of the domains of convexified functions and the approximate construction of the upper convex hull of a function as the lower envelope of a finite set of support hyperplanes of its subgraph.

Author keywords:

optimal control; differential games; numerical methods LINEAR-DIFFERENTIAL GAMES; PROGRAM SYNTHESIS; CONFLICT CONTROL; CONSTRUCTION; RESTRICTIONS; ALGORITHMS; PAYOFF

DOI:

10.1134/S0081543815090060

Web of Science ID:

ISI:000366347200006

Соавторы в МНС:

—

Другие поля

Поле	Значение
Month	DEC
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Keywords-Plus	LINEAR-DIFFERENTIAL GAMES; PROGRAM SYNTHESIS; CONFLICT CONTROL; CONSTRUCTION; RESTRICTIONS; ALGORITHMS; PAYOFF
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	m.i.gomoyunov@gmail.com d.v.kornev@gmail.com nyul@imm.uran.ru
ResearcherID-Numbers	Gomoyunov, Mikhail/N-7759-2016 Lukoyanov , Nikolai/Q-6872-2016
Funding-Acknowledgement	Presidium of Russian Academy of Sciences ``Dynamic Systems and Control Theory,{''}; Ural Branch of Russian Academy of Sciences {[}12-P-1-1002]; Russian Foundation for Basic Research {[}12-01-00290-a, 14-01-31319-mol\_a]
Funding-Text	This work was supported by the Program of the Presidium of the Russian Academy of Sciences ``Dynamic Systems and Control Theory,{''} by the Ural Branch of the Russian Academy of Sciences (project no. 12-P-1-1002), and by the Russian Foundation for Basic Research (project nos. 12-01-00290-a and 14-01-31319-mol\_a).
Number-of-Cited-References	30
Usage-Count-Since-2013	5
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	CY3ZA