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On the Inverse Problem for Robust Capture Zone Construction

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  • V. Y. Glizer

    (Israel Institute of Technology)

  • V. Turetsky

    (Israel Institute of Technology)

Abstract

An interception problem with variable velocities and variable lateral acceleration boundaries is considered. Two problems, inverse to constructing the capture zone for a given linear strategy, are formulated. In the first (weak) formulation, a linear strategy is derived forcing its capture zone to contain a given set. In the second (strong) formulation, the capture zone of such a linear strategy is forced to coincide with a given set. A step-by-step algorithm, solving these problems, is derived. This algorithm is based on a detailed differential-geometrical analysis of the capture zone boundary. Illustrative examples are presented.

Suggested Citation

  • V. Y. Glizer & V. Turetsky, 2008. "On the Inverse Problem for Robust Capture Zone Construction," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 381-400, May.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:2:d:10.1007_s10957-007-9337-3
    DOI: 10.1007/s10957-007-9337-3
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    References listed on IDEAS

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    1. Vladimir Turetsky & Valery Y. Glizer, 2005. "Continuous Feedback Control Strategy With Maximal Capture Zone In A Class Of Pursuit Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-24.
    2. V. Turetsky, 2007. "Capture Zones of Cheap Control Interception Strategies," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 69-84, October.
    3. V. Turetsky, 2004. "Upper Bounds of the Pursuer Control Based on a Linear-Quadratic Differential Game," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 163-191, April.
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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.

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