On the question of construction of an attraction set under constraints of asymptotic nature

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• 作者：A. G. Chentsov ; A. P. Baklanov
• 关键词：filter base ; finitely additive measure ; attraction set ; generalized element ; ultrafilter
• 刊名：Proceedings of the Steklov Institute of Mathematics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：291
• 期：1-supp
• 页码：40-55
• 全文大小：308 KB
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• 作者单位：A. G. Chentsov (1) (3)
  A. P. Baklanov (1) (2)
  
  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia
  3. Institute of Radioelectronics and Information Technologies, Ural Federal University, ul. Mira 19, Yekaterinburg, 620002, Russia
  2. International Institute for Applied Systems Analysis, Schlossplatz 1, A-2361, Laxenburg, Austria
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8605

文摘

We study a variant of the reachability problem with constraints of asymptotic character on the choice of controls. More exactly, we consider a control problem in the class of impulses of given intensity and vanishingly small length. The situation is complicated by the presence of discontinuous dependences, which produce effects of the type of multiplying a discontinuous function by a generalized function. The constructed extensions in the special class of finitely additive measures make it possible to present the required solution, defined as an asymptotic analog of a reachable set, in terms of a continuous image of a compact, which is described with the use of the Stone space corresponding to the natural algebra of sets of the control interval. One of the authors had the honor of communicating with Nikolai Nikolaevich Krasovskii for many years and discussed with him problems that led to the statement considered in the paper. Krasovskii’s support of this research direction provided possibilities for its fruitful development. His disciples and colleagues will always cherish the memory of Nikolai Nikolaevich in their hearts. Keywords filter base finitely additive measure attraction set generalized element ultrafilter