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Synthesis of Optimal Bang–Bang Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Linear Speeds

Author

Listed:
  • T. Tarnopolskaya

    (CSIRO Mathematics, Informatics and Statistics)

  • N. Fulton

    (CSIRO Mathematics, Informatics and Statistics)

  • H. Maurer

    (Münster University)

Abstract

Close proximity encounters most often occur for situations in which participants have unequal linear speeds. Cooperative collision avoidance strategies for such situations are investigated. We show that, unlike the encounters of participants with equal linear speeds, bang–bang collision avoidance strategies are not always optimal when the linear speeds are unequal, and we establish the conditions for which no optimal bang–bang controls exist near the terminal time. Nevertheless, under certain conditions, we demonstrate that bang–bang collision avoidance strategies remain optimal for encounters of participants with unequal linear speeds. Such conditions are established, and it appears that they cover a wide range of important practical situations. The synthesis of bang–bang control is constructed, and its optimality is established.

Suggested Citation

  • T. Tarnopolskaya & N. Fulton & H. Maurer, 2012. "Synthesis of Optimal Bang–Bang Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Linear Speeds," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 115-144, October.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:1:d:10.1007_s10957-012-0049-y
    DOI: 10.1007/s10957-012-0049-y
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    References listed on IDEAS

    as
    1. T. Tarnopolskaya & N. Fulton, 2010. "Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 367-390, February.
    2. A. Miele & T. Wang & J. A. Mathwig & M. Ciarcià, 2010. "Collision Avoidance for an Aircraft in Abort Landing: Trajectory Optimization and Guidance," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 233-254, August.
    3. A. Miele & T. Wang & C. S. Chao & J. B. Dabney, 1999. "Optimal Control of a Ship for Course Change and Sidestep Maneuvers," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 259-282, November.
    4. Clements, John C., 1999. "The optimal control of collision avoidance trajectories in air traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 265-280, May.
    5. Babikian, Raffi & Lukachko, Stephen P. & Waitz, Ian A., 2002. "The historical fuel efficiency characteristics of regional aircraft from technological, operational, and cost perspectives," Journal of Air Transport Management, Elsevier, vol. 8(6), pages 389-400.
    6. A. Miele & T. Wang, 2006. "Optimal Trajectories and Guidance Schemes for Ship Collision Avoidance," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 1-21, April.
    7. A. Miele & T. Wang & C. S. Chao & J. B. Dabney, 1999. "Optimal Control of a Ship for Collision Avoidance Maneuvers," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 495-519, December.
    8. T. Tarnopolskaya & N. Fulton, 2009. "Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 355-375, February.
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    Cited by:

    1. Erick J. Rodríguez-Seda & Dušan M. Stipanović & Mark W. Spong, 2016. "Guaranteed Collision Avoidance for Autonomous Systems with Acceleration Constraints and Sensing Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 1014-1038, March.

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