Method of resolving functions in the theory of conflict-controlled processes

The method of resolving functions is analyzed concerning the theory of conflict-controlled processes. Inverse Minkowski functionals play the key role. They are used to form special multivalued mappings and corresponding resolving functions, closely related to the parameters of the original conflict-...

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Bibliographic Details
Published in:Cybernetics and systems analysis Vol. 48; no. 4; pp. 512 - 531
Main Authors: Chikrii, A. A., Rappoport, I. S.
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2012
Springer
Springer Nature B.V
Subjects:
Algebra
Artificial Intelligence
Construction
Control
Control systems
Cybernetics
Euclidean space
Functionals
Game theory
Games
Inverse
Mapping
Mathematics
Mathematics and Statistics
Methods
Processor Architectures
Selectors
Software Engineering/Programming and Operating Systems
Studies
Systems Analysis
Systems Theory
Ukraine
conflict-controlled process
support function
measurable selector
guaranteed time
superpositional measurability
Minkowski function
stroboscopic strategy
multivalued mapping
Pontryagin condition
ISSN:1060-0396, 1573-8337
Online Access:Get full text
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Summary:The method of resolving functions is analyzed concerning the theory of conflict-controlled processes. Inverse Minkowski functionals play the key role. They are used to form special multivalued mappings and corresponding resolving functions, closely related to the parameters of the original conflict-controlled process. A modern technique of the theory of multivalued mappings is effectively used to substantiate game constructions and get substantial results on their basis. The problems related to the properties of special multivalued mappings and their selectors, which play a crucial role in proving the assertions, are brought into the foreground.
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-012-9430-y