Games of simple pursuit and approach on a two-dimensional cone

A. A. Melikyan; N. V. Ovakimyan; L. L. Harutiunian

doi:10.1023/A:1022692227722

Games of simple pursuit and approach on a two-dimensional cone

A. A. Melikyan
, N. V. Ovakimyan
, L. L. Harutiunian

Research output: Contribution to journal › Article › peer-review

Abstract

The complete solution of two differential games with simple motion on a two-dimensional cone is presented. The method of generalized (singular) characteristics is used for the analysis of singular paths. The level lines of the game value and optimal phase portrait are constructed, and the latter is shown to include several types of singular surfaces (dispersal, equivocal, universal). An algorithm is developed for the construction of the synthesis for both players and is used in computer simulation.

Original language	English (US)
Pages (from-to)	515-543
Number of pages	29
Journal	Journal of Optimization Theory and Applications
Volume	98
Issue number	3
DOIs	https://doi.org/10.1023/A:1022692227722
State	Published - Sep 1998
Externally published	Yes

Keywords

Differential games
Geodesic lines
Singular characteristics
Singular paths
Smooth manifolds

ASJC Scopus subject areas

Management Science and Operations Research
Control and Optimization
Applied Mathematics

Online availability

10.1023/A:1022692227722

Library availability

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title = "Games of simple pursuit and approach on a two-dimensional cone",

abstract = "The complete solution of two differential games with simple motion on a two-dimensional cone is presented. The method of generalized (singular) characteristics is used for the analysis of singular paths. The level lines of the game value and optimal phase portrait are constructed, and the latter is shown to include several types of singular surfaces (dispersal, equivocal, universal). An algorithm is developed for the construction of the synthesis for both players and is used in computer simulation.",

keywords = "Differential games, Geodesic lines, Singular characteristics, Singular paths, Smooth manifolds",

author = "Melikyan, \{A. A.\} and Ovakimyan, \{N. V.\} and Harutiunian, \{L. L.\}",

note = "'This work was supported by the International Science Foundation, Grant RYT000 and by the Russian Fund for Fundamental Research, Grant 95-01-00802. 2Leading Research Fellow, Institute of Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia. 3Research Fellow, Institute of Mechanics, National Academy of Sciences, Yerevan, Republic of Armenia. 4Associate Professor, Yerevan State University, Yerevan, Republic of Armenia.",

year = "1998",

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doi = "10.1023/A:1022692227722",

language = "English (US)",

volume = "98",

pages = "515--543",

journal = "Journal of Optimization Theory and Applications",

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AU - Melikyan, A. A.

AU - Ovakimyan, N. V.

AU - Harutiunian, L. L.

N1 - 'This work was supported by the International Science Foundation, Grant RYT000 and by the Russian Fund for Fundamental Research, Grant 95-01-00802. 2Leading Research Fellow, Institute of Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia. 3Research Fellow, Institute of Mechanics, National Academy of Sciences, Yerevan, Republic of Armenia. 4Associate Professor, Yerevan State University, Yerevan, Republic of Armenia.

PY - 1998/9

Y1 - 1998/9

N2 - The complete solution of two differential games with simple motion on a two-dimensional cone is presented. The method of generalized (singular) characteristics is used for the analysis of singular paths. The level lines of the game value and optimal phase portrait are constructed, and the latter is shown to include several types of singular surfaces (dispersal, equivocal, universal). An algorithm is developed for the construction of the synthesis for both players and is used in computer simulation.

AB - The complete solution of two differential games with simple motion on a two-dimensional cone is presented. The method of generalized (singular) characteristics is used for the analysis of singular paths. The level lines of the game value and optimal phase portrait are constructed, and the latter is shown to include several types of singular surfaces (dispersal, equivocal, universal). An algorithm is developed for the construction of the synthesis for both players and is used in computer simulation.

KW - Differential games

KW - Geodesic lines

KW - Singular characteristics

KW - Singular paths

KW - Smooth manifolds

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ER -

Games of simple pursuit and approach on a two-dimensional cone

Abstract

Keywords

ASJC Scopus subject areas

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