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Computing the Minimum-Time Interception of a Moving Target

Author

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  • Maksim Buzikov

    (V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences)

Abstract

In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must approach a moving target whose trajectory is known a priori. Our framework employs an analytical description of the distance from an arbitrary point to the reachable set of the plant. The proposed algorithm is always convergent and cannot be improved without losing the guarantee of its convergence to the correct solution for arbitrary Lipschitz continuous trajectories of the moving target. In practice, it is difficult to obtain an analytical description of the distance to the reachable set for the sophisticated state equation of the plant. Nevertheless, it was shown that the distance can be obtained for some widely used models, such as the Dubins car, in an explicit form. Finally, we illustrate the generality and effectiveness of the proposed framework for simple motions and the Dubins model.

Suggested Citation

  • Maksim Buzikov, 2024. "Computing the Minimum-Time Interception of a Moving Target," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 975-995, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02487-2
    DOI: 10.1007/s10957-024-02487-2
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    References listed on IDEAS

    as
    1. C. Yalçın Kaya, 2017. "Markov–Dubins path via optimal control theory," Computational Optimization and Applications, Springer, vol. 68(3), pages 719-747, December.
    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.
    Full references (including those not matched with items on IDEAS)

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