Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit

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Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit. / Mikhalev, D. k.; Ushakov, V. n.
In: Automation and Remote Control, Vol. 68, No. 11, 01.11.2007, p. 2056-2070.

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

BibTeX

@article{75a7599d161d43448ac14b2088b913bf,

title = "Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit",

abstract = "Consideration is given to the differential game on the finite period of time in which the first player has to guarantee that the phase point will entry the terminal set and the second one must ensure the evasion of the terminal set on this interval. Is proposed a method for approximate construction of the set of positional absorption, i.e, the set of all initial points for which the problem of pursuit posed for the first player is solvable. The method is based on unification constructions and structures close to them. Relations defining the system of sets that approximates the set of positional absorption are written out. The convergence of the approximating system to the set of positional absorption is proved.",

author = "Mikhalev, {D. k.} and Ushakov, {V. n.}",

note = "This work was supported by the Russian Foundation for Basic Research, projects nos. 05-01-00601 a and 04-01-96099ural a and the Russian Federation President Grant “State Support for Leading Scientific Schools,” project no. NSh-8512.2006.1.",

year = "2007",

month = nov,

day = "1",

doi = "10.1134/S0005117907110136",

language = "English",

volume = "68",

pages = "2056--2070",

journal = "Automation and Remote Control",

issn = "0005-1179",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "11",

}

RIS

TY - JOUR

T1 - Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit

AU - Mikhalev, D. k.

AU - Ushakov, V. n.

N1 - This work was supported by the Russian Foundation for Basic Research, projects nos. 05-01-00601 a and 04-01-96099ural a and the Russian Federation President Grant “State Support for Leading Scientific Schools,” project no. NSh-8512.2006.1.

PY - 2007/11/1

Y1 - 2007/11/1

N2 - Consideration is given to the differential game on the finite period of time in which the first player has to guarantee that the phase point will entry the terminal set and the second one must ensure the evasion of the terminal set on this interval. Is proposed a method for approximate construction of the set of positional absorption, i.e, the set of all initial points for which the problem of pursuit posed for the first player is solvable. The method is based on unification constructions and structures close to them. Relations defining the system of sets that approximates the set of positional absorption are written out. The convergence of the approximating system to the set of positional absorption is proved.

AB - Consideration is given to the differential game on the finite period of time in which the first player has to guarantee that the phase point will entry the terminal set and the second one must ensure the evasion of the terminal set on this interval. Is proposed a method for approximate construction of the set of positional absorption, i.e, the set of all initial points for which the problem of pursuit posed for the first player is solvable. The method is based on unification constructions and structures close to them. Relations defining the system of sets that approximates the set of positional absorption are written out. The convergence of the approximating system to the set of positional absorption is proved.

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U2 - 10.1134/S0005117907110136

DO - 10.1134/S0005117907110136

M3 - Article

VL - 68

SP - 2056

EP - 2070

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 11

ER -

ID: 41300378