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Optimal Control of Several Motion Models

Author

Listed:
  • Tan H. Cao

    (SUNY Korea)

  • Nilson Chapagain

    (SUNY Korea)

  • Haejoon Lee

    (SUNY Korea)

  • Thi Phung

    (Wayne State University)

  • Nguyen Nang Thieu

    (SUNY Korea
    Institute of Mathematics, Vietnam Academy of Science and Technology)

Abstract

This paper is devoted to studying the dynamic optimization of several controlled crowd motion models in general planar settings. A set of necessary optimality conditions for optimal control problems involving crowd motion models with multiple agents and obstacles was derived and thoroughly analyzed. The analysis provides valuable insights into the primal and dual elements, as well as the degeneracy phenomena. The paper proposes several effective algorithms based on these necessary optimality conditions and presents various nontrivial illustrative examples along with their simulations. The implementation of all the considered motion models can be found via the link: https://github.com/tancao1128/Optimal_Control_of_Several_Motion_Models .

Suggested Citation

  • Tan H. Cao & Nilson Chapagain & Haejoon Lee & Thi Phung & Nguyen Nang Thieu, 2025. "Optimal Control of Several Motion Models," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-36, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02610-x
    DOI: 10.1007/s10957-025-02610-x
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    References listed on IDEAS

    as
    1. Giovanni Colombo & Boris Mordukhovich & Dao Nguyen, 2019. "Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 439-472, August.
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