A Modified Method of Resolving Functions for Game Control Problems with Integral Constraints

The authors consider linear differential games with integral constraints. Sufficient conditions for the game termination in a finite guaranteed time are formulated for the case where the Nikolsky condition is not satisfied. Multivalued mappings that generate the upper and lower resolving functions o...

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Veröffentlicht in:Cybernetics and systems analysis Jg. 59; H. 4; S. 581 - 590
Hauptverfasser: Chikrii, A. A, Rappoport, I. S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2023
Springer
Springer Nature B.V
Schlagworte:
Artificial Intelligence
Constraints
Control
Cybernetics
Differential games
Integral equations
Mathematics
Mathematics and Statistics
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
linear differential game
stroboscopic strategy
multivalued mapping
integral constraints
resolving functions
ISSN:1060-0396, 1573-8337
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Zusammenfassung:The authors consider linear differential games with integral constraints. Sufficient conditions for the game termination in a finite guaranteed time are formulated for the case where the Nikolsky condition is not satisfied. Multivalued mappings that generate the upper and lower resolving functions of special type are introduced. The modified schemes of the Nikolsky direct method and the method of resolving functions are proposed, which ensure the game termination in a finite guaranteed time in the class of quasi-strategies and stroboscopic strategies. The most recent theoretical results are illustrated by the reference Pontryagin’s example with objects of the same type.
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-023-00593-z