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Robust Solution Of A Time-Variable Interception Problem: A Cheap Control Approach

Author

Listed:
  • VLADIMIR TURETSKY

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

  • VALERY Y. GLIZER

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

Abstract

A planar interception problem of a maneuverable target is considered using the linearized kinematic model with variable velocities and first-order dynamics of the interceptor and target. The maneuverabilities of the interceptor and target are assumed to be variable. By using an auxiliary zero-sum linear-quadratic differential game with cheap controls of both players, an interception guidance law, linear with respect to the state vector, is derived. An analytical description of the set of initial positions (capture set) is obtained, from which this guidance law provides zero miss distance, subject to given maneuverabilities of the interceptor and target. A numerical example illustrating the analytical results is presented.

Suggested Citation

  • Vladimir Turetsky & Valery Y. Glizer, 2007. "Robust Solution Of A Time-Variable Interception Problem: A Cheap Control Approach," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 637-655.
    • Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:04:n:s0219198907001631
    DOI: 10.1142/S0219198907001631
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    Cited by:

    1. V. Y. Glizer & V. Turetsky, 2010. "Robust Transferable Sets of Linear Transferring Strategies," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 36-52, April.

    More about this item

    Keywords

    Interception; guidance law; differential game; cheap control; capture set;
    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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