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

Jhanani Selvakumar () and Efstathios Bakolas ()
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Jhanani Selvakumar: The University of Texas at Austin
Efstathios Bakolas: The University of Texas at Austin

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 1, No 12, 240-264

Abstract: 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.

Keywords: Pursuit–evasion game; Time-varying winds; Minimum-time guidance; Input constraints; 91A23; 49N90; 49N75 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1326-1

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