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Optimal Evasion from a Pursuer with Delayed Information

Author

Listed:
  • V. Y. Glizer

    (Technion-Israel Institute of Technology)

  • J. Shinar

    (Technion-Israel Institute of Technology)

Abstract

A class of prescribed duration pursuit–evasion problems with first-order acceleration dynamics and bounded controls is considered. In this class, the pursuer has delayed information on the lateral acceleration of the evader, but knows perfectly the other state variables. Moreover, the pursuer applies a strategy derived from the perfect information pursuit–evasion game solution. Assuming that the evader has perfect information on all the state variables as well as on the delay of the pursuer and its strategy, an optimal evasion problem is formulated. The necessary optimality conditions indicate that the evader optimal control has a bang–bang structure. Based on this result, two particular cases of the pursuer strategy (continuous and piecewise continuous in the state variables) are considered for the solution of the optimal evasion problem. In the case of the continuous pursuer strategy, the switch point of the optimal control can be obtained as a root of the switch function. However, in the case of the piecewise continuous (bang–bang) pursuer strategy, this method fails, because of the discontinuity of the switch function at this very point. In this case, a direct method for obtaining the switch point, based on the structure of the solution, is proposed. Numerical results illustrating the theoretical analysis are presented leading to a comparison of the two cases.

Suggested Citation

  • V. Y. Glizer & J. Shinar, 2001. "Optimal Evasion from a Pursuer with Delayed Information," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 7-38, October.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:1:d:10.1023_a:1017515129544
    DOI: 10.1023/A:1017515129544
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    References listed on IDEAS

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    1. Josef Shinar & Valery Y. Glizer, 1999. "Solution Of A Delayed Information Linear Pursuit-Evasion Game With Bounded Controls," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 197-217.
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    Cited by:

    1. Tiago Roux Oliveira & Victor Hugo Pereira Rodrigues & Miroslav Krstić & Tamer Başar, 2021. "Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 700-735, December.

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