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Robust Time-Optimal Guidance in a Partially Uncertain Time-Varying Flow-Field

Author

Listed:
  • Jhanani Selvakumar

    (The University of Texas at Austin)

  • Efstathios Bakolas

    (The University of Texas at Austin)

Abstract

In this paper, we address the problem of guiding an aerial or aquatic vehicle to a fixed target point in a partially uncertain flow-field. We assume that the motion of the vehicle is described by a point-mass linear kinematic model. In addition, the velocity of the flow-field, which is taken to be time varying, can be decomposed into two components: one which is known a priori and another one which is uncertain and only a bound on its magnitude is known. We show that the guidance problem can be reformulated as an equivalent pursuit evasion game with time-varying affine dynamics. To solve the latter game, we propose an extension of a specialized solution approach, which transforms the pursuit–evasion game (whose terminal time is free) via a special state transformation into a family of games with fixed terminal time. In addition, we provide a simple method to visualize the level sets of the value function of the game, along with the corresponding reachable sets. Furthermore, we compare our conservative game-theoretic solution with a pure optimal control solution, for the special case in which the flow-field is perfectly known a priori.

Suggested Citation

  • Jhanani Selvakumar & Efstathios Bakolas, 2018. "Robust Time-Optimal Guidance in a Partially Uncertain Time-Varying Flow-Field," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 240-264, October.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1326-1
    DOI: 10.1007/s10957-018-1326-1
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    References listed on IDEAS

    as
    1. Christian M. Chilan & Bruce A. Conway, 2015. "A Reachable Set Analysis Method for Generating Near-Optimal Trajectories of Constrained Multiphase Systems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 161-194, October.
    2. Efstathios Bakolas, 2014. "Optimal Guidance of the Isotropic Rocket in the Presence of Wind," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 954-974, September.
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