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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Bibliographic Details
Published in:Cybernetics and systems analysis Vol. 59; no. 2; pp. 251 - 265
Main Authors: Chikrii, A. A., Rappoport, I. S.
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2023
Springer
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-023-00559-1