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Home » Issues » Archive of Issues » 2017 - 1 issue » pp. 69-85

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Russia Chelyabinsk
Year
2017
Volume
27
Issue
1
Pages
69-85
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Section Mathematics
Title Synthesis of controls in a single-type game problem of pulse meeting at fixed time with a terminal set in the form of a ring
Author(-s) Ukhobotov V.I.a, Izmest'ev I.V.a
Affiliations Chelyabinsk State Universitya
Abstract We consider a linear differential game with a pulse control of the first player. The abilities of the first player are determined by the stock of resources that the player can use when forming his control. At certain instants of time a separation of part of the resources stock is possible, which may implicate an “instantaneous” change of a phase vector, resulting in the complication of the problem. The control of the second player has geometrical constraints. The vectograms of the players are described by the same ball with different time-dependent radii. The terminal set of the game is determined by the condition of belonging the norm of a phase vector to a segment with positive ends. In this paper, a set defined by this condition is called a ring. The aim of the first player is to lead a phase vector to the terminal set at fixed time. The aim of the second player is opposite. With the maximal stable bridge, which has been defined by the authors previously, optimal controls of players are constructed.
Keywords pulse control, optimal control, differential game
UDC 517.977.80
MSC 91A23, 49N75
DOI 10.20537/vm170107
Received 12 December 2016
Language Russian
Citation Ukhobotov V.I., Izmest'ev I.V. Synthesis of controls in a single-type game problem of pulse meeting at fixed time with a terminal set in the form of a ring, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 1, pp. 69-85.
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