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Solvability Of Linear-Quadratic Differential Games Associated With Pursuit-Evasion Problems

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Author Info

  • JOSEF SHINAR

    ()
    (Faculty of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa 32000, Israel)

  • VLADIMIR TURETSKY

    ()
    (Faculty of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa 32000, Israel)

  • VALERY Y. GLIZER

    ()
    (Department of Mathematics, Ort Braude College, P.O. Box 78, Karmiel 21982, Israel)

  • EDUARD IANOVSKY

    ()
    (Faculty of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa 32000, Israel)

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    Abstract

    A finite horizon zero-sum linear-quadratic differential game with a generalized cost functional, involving a Lebesgue integral with a measure that has both discrete and distributed parts, is considered. Sufficient conditions for the solvability of such a game are established in terms of the eigenvalues of an integral operator in Hilbert space. The game solution is based on solving an impulsive Riccati matrix differential equation. These results are applied for two games associated with pursuit-evasion problems. Illustrative examples are presented.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 10 (2008)
    Issue (Month): 04 ()
    Pages: 481-515

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    Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:04:p:481-515

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    Related research

    Keywords: Linear-quadratic differential game; solvability conditions; pursuit-evasion; Subject Classification: 49N70; Subject Classification: 49N90; Subject Classification: 91A23;

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