Modified Resolving-Functions Method for Game Problems of Approach of Controlled Objects with Different Inertia

The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin’s condition is not satisfied are formulated. Some shift functions are considered instead of...

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Vydáno v:Cybernetics and systems analysis Ročník 59; číslo 2; s. 251 - 265
Hlavní autoři: Chikrii, A. A., Rappoport, I. S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.03.2023
Springer
Springer Nature B.V
Témata:
Artificial Intelligence
Control
Cybernetics
Games
Inertia
Mathematics
Mathematics and Statistics
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
quasi-linear differential game
resolving function
multi-valued mapping
stroboscopic strategy
controlled objects with different inertia
measurable selector
ISSN:1060-0396, 1573-8337
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Abstract The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin’s condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multi-valued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type, and based on them, two types of modified schemes are proposed: the scheme of Pontryagin’s first method and the method of resolving functions. This ensures the completion of the conflict-controlled process for objects with different inertia in the class of quasi-strategies and counter-controls. New theoretical results are illustrated by a model example.
AbstractList The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin’s condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multi-valued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type, and based on them, two types of modified schemes are proposed: the scheme of Pontryagin’s first method and the method of resolving functions. This ensures the completion of the conflict-controlled process for objects with different inertia in the class of quasi-strategies and counter-controls. New theoretical results are illustrated by a model example.
The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin's condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multi-valued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type, and based on them, two types of modified schemes are proposed: the scheme of Pontryagin's first method and the method of resolving functions. This ensures the completion of the conflict- controlled process for objects with different inertia in the class of quasi-strategies and counter- controls. New theoretical results are illustrated by a model example. Keywords: controlled objects with different inertia, quasi-linear differential game, multi-valued mapping, measurable selector, stroboscopic strategy, resolving function.
Audience Academic
Author Chikrii, A. A.
Rappoport, I. S.
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Cites_doi 10.1615/JAutomatInfScien.v48.i3.30
10.1007/s10559-012-9430-y
10.1007/s10559-021-00355-9
10.1515/9781400873173
10.1134/S0081543810040073
ContentType Journal Article
Copyright Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
COPYRIGHT 2023 Springer
Springer Science+Business Media, LLC, part of Springer Nature 2023.
Copyright_xml – notice: Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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Keywords quasi-linear differential game
resolving function
multi-valued mapping
stroboscopic strategy
controlled objects with different inertia
measurable selector
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RappoportISMethod of resolving functions for game problems of approach of controlled objects with different inertiaCybern. Syst. Analysis202157229631210.1007/s10559-021-00355-91470.91045
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IoffeADTikhomirovVMTheory of Extremum Problems1974MoscowNauka[in Russian]
ChikriiAAAn analytical method in dynamic pursuit gamesProc. Steklov Inst. of Mathematics20102716985284171310.1134/S00815438100400731302.49052
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RockafellarRTConvex Analysis1970PrincetonPrinceton Univ. Press10.1515/97814008731730193.18401
HajekOPursuit Games1975New YorkAcad. Press0324.90104
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– reference: RappoportISMethod of resolving functions for game problems of approach of controlled objects with different inertiaCybern. Syst. Analysis202157229631210.1007/s10559-021-00355-91470.91045
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SubjectTerms Artificial Intelligence
Control
Cybernetics
Games
Inertia
Mathematics
Mathematics and Statistics
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
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Title Modified Resolving-Functions Method for Game Problems of Approach of Controlled Objects with Different Inertia
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Volume 59
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