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Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle

Author

Listed:
  • Andrey A. Galyaev

    (Institute of Control Sciences of RAS, 117997 Moscow, Russia)

  • Pavel V. Lysenko

    (Institute of Control Sciences of RAS, 117997 Moscow, Russia)

  • Evgeny Y. Rubinovich

    (Institute of Control Sciences of RAS, 117997 Moscow, Russia)

Abstract

This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation.

Suggested Citation

  • Andrey A. Galyaev & Pavel V. Lysenko & Evgeny Y. Rubinovich, 2021. "Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle," Mathematics, MDPI, vol. 9(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2386-:d:642984
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    Cited by:

    1. Natalia Bakhtadze, 2023. "Preface to the Special Issue on “Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control”—Special Issue Book," Mathematics, MDPI, vol. 11(8), pages 1-3, April.

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