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Nonanticipating Multimappings and Their Construction by the Method of Program Iterations: I

Nonanticipating Multimappings and Their Construction by the Method of Program Iterations: I Di erential Equations, Vol. 37, No. 4, 2001, pp. 498{509. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 4, 2001, pp. 470{480. Original Russian Text Copyright c 2001 by Chentsov. ORDINARY DIFFERENTIAL EQUATIONS Nonanticipating Multimappings and Their Construction by the Method of Program Iterations: I A. G. Chentsov Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, Yekaterinburg, Russia Received September 4, 2000 We consider the problem of nding nonanticipating multiselectors of multimappings. We in- vestigate an iterative procedure for reducing a multimapping to a nonanticipating multimapping that is a multivalued selector of the original multimapping. In control problems, nonanticipat- ing multimappings are treated as multivalued strategies, which are used in the formalization of a di erential game. Under natural conditions of information coordination, this formalization is equivalent to Krasovskii's positional formalization (in the framework of the latter, Krasovskii and Subbotin proved the fundamental theorem on the alternative in the pursuit-evasion di eren- tial game). The procedure suggested below goes back to the so-called method of program iterations, which was used in the construction of stable bridges (which play an important role in the theorem on the alternative) and the value function in a di erential game. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Nonanticipating Multimappings and Their Construction by the Method of Program Iterations: I

Differential Equations , Volume 37 (4) – Oct 12, 2004

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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1019275422741
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 37, No. 4, 2001, pp. 498{509. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 4, 2001, pp. 470{480. Original Russian Text Copyright c 2001 by Chentsov. ORDINARY DIFFERENTIAL EQUATIONS Nonanticipating Multimappings and Their Construction by the Method of Program Iterations: I A. G. Chentsov Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, Yekaterinburg, Russia Received September 4, 2000 We consider the problem of nding nonanticipating multiselectors of multimappings. We in- vestigate an iterative procedure for reducing a multimapping to a nonanticipating multimapping that is a multivalued selector of the original multimapping. In control problems, nonanticipat- ing multimappings are treated as multivalued strategies, which are used in the formalization of a di erential game. Under natural conditions of information coordination, this formalization is equivalent to Krasovskii's positional formalization (in the framework of the latter, Krasovskii and Subbotin proved the fundamental theorem on the alternative in the pursuit-evasion di eren- tial game). The procedure suggested below goes back to the so-called method of program iterations, which was used in the construction of stable bridges (which play an important role in the theorem on the alternative) and the value function in a di erential game.

Journal

Differential EquationsSpringer Journals

Published: Oct 12, 2004

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