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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 3, Pages 241–261
(Mi timm418)
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On the result equivalence of constraints of asymptotic nature
A. G. Chentsov Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
An abstract control problem with constraints of integral nature is considered. Conditions are established for the equivalence of different variants of asymptotic constraints corresponding to weakening the traditional constraints on the choice of the controls. The proposed approach is based on an extension construction in the class of finitely additive measures. For a long time, the author has had the wonderful opportunity to discuss his results concerning the mentioned (rather nontraditional) approach with N. N. Krasovskii; these discussions and the support of this approach by N. N. Krasovskii played an important role in its formation and development.
Keywords:
finitely additive measure, attraction set, net.
Received: 02.10.2008
Citation:
A. G. Chentsov, “On the result equivalence of constraints of asymptotic nature”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 3, 2009, 241–261; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S32–S53
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https://www.mathnet.ru/eng/timm418 https://www.mathnet.ru/eng/timm/v15/i3/p241
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Abstract page: | 381 | Full-text PDF : | 93 | References: | 105 | First page: | 1 |
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