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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Josef Shinar & Vladimir Turetsky & Valery Y. Glizer & Eduard Ianovsky, 2008. "Solvability Of Linear-Quadratic Differential Games Associated With Pursuit-Evasion Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 481-515.
    • Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:04:n:s0219198908002060
    DOI: 10.1142/S0219198908002060
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    Citations

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    Cited by:

    1. Vladimir Turetsky, 2016. "Robust Route Realization by Linear-Quadratic Tracking," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 977-992, September.

    More about this item

    Keywords

    Linear-quadratic differential game; solvability conditions; pursuit-evasion; Subject Classification: 49N70; Subject Classification: 49N90; Subject Classification: 91A23;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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