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Russia Yekaterinburg
Year
2020
Volume
30
Issue
4
Pages
553-571
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Section Mathematics
Title Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances
Author(-s) Gomoyunov M.I.ab, Serkov D.A.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract For a dynamical system controlled under conditions of disturbances, a problem of optimizing the guaranteed result is considered. A feature of the problem is the presence of functional constraints on disturbances, under which, in general, the set of admissible disturbances is not closed with respect to the operation of “gluing up” of two of its elements. This circumstance does not allow to apply directly the methods developed within the differential games theory for studying the problem and, thus, leads to the necessity of modifying them appropriately. The paper provides a new notion of a non-anticipative control strategy. It is proved that the corresponding functional of the optimal guaranteed result satisfies the dynamic programming principle. As a consequence, so-called properties of $u$- and $v$-stability of this functional are established, which may allow, in the future, to obtain a constructive solution of the problem in the form of feedback (positional) controls.
Keywords guarantee optimization, functional constraints, non-anticipative strategies, dynamic programming principle
UDC 517.977
MSC 49N70, 49L20, 93C15
DOI 10.35634/vm200402
Received 31 August 2020
Language English
Citation Gomoyunov M.I., Serkov D.A. Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 4, pp. 553-571.
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