Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/51354
Title: An estimate of the stability defect for a positional absorption set subjected to discriminant transformations
Authors: Ushakov, V. N.
Uspenskii, A. A.
Malev, A. G.
Issue Date: 2012
Citation: Ushakov V. N. An estimate of the stability defect for a positional absorption set subjected to discriminant transformations / V. N. Ushakov, A. A. Uspenskii, A. G. Malev // Proceedings of the Steklov Institute of Mathematics. — 2012. — Vol. 279. — № 1. — P. 113-129.
Abstract: We study bordering "paths," i. e., sets in the position space of an approach-evasion differential game that contain the positional absorption set. The positional absorption set provides an exact (classical) solution of the game. At the same time, its boundary is nonsmooth, which complicates the construction of this set. On the contrary, a set different from the positional absorption set may not provide an exact solution of the game but can be constructed with relative ease, for example, with the help of analytical formulas. There may be other reasons for using "paths" in solving a game. For example, the smoothness of the boundary of a chosen "path" allows one to efficiently form the players' control procedures guaranteeing the solution of a game problem in a "soft" setting by taking the motion of a conflict-control system to a neighborhood of the target set. In this paper, we propose a procedure for smoothing a set in a part of variables; the procedure is based on discriminant transformations. We study the stability defect caused by replacing the positional absorption set of a differential game by a set-"path" with boundary that is smooth in the space variables. An estimate for the stability defect of the constructed set is presented. The results are illustrated by the example of a known differential game. © 2012 Pleiades Publishing, Ltd.
Keywords: APPROACH GAME PROBLEM
CONFLICT-CONTROL SYSTEM
CONTROL
HAMILTONIAN
STABLE BRIDGE
URI: http://hdl.handle.net/10995/51354
https://elar.urfu.ru/handle/10995/51354
metadata.dc.rights: info:eu-repo/semantics/restrictedAccess
SCOPUS ID: 84871321990
WOS ID: 000312634700009
PURE ID: 1069706
ISSN: 0081-5438
DOI: 10.1134/S008154381209009X
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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