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A Maximum Principle for Optimal Control Problems Involving Sweeping Processes with a Nonsmooth Set

Author

Listed:
  • Maria do Rosário de Pinho

    (SYSTEC, ARISE, Faculdade de Engenharia da Universidade do Porto)

  • Maria Margarida A. Ferreira

    (SYSTEC, ARISE, Faculdade de Engenharia da Universidade do Porto)

  • Georgi Smirnov

    (University of Minho, Physics Center of Minho and Porto Universities (CF-UM-UP))

Abstract

We generalize a maximum principle for optimal control problems involving sweeping systems previously derived in de Pinho et al. (Optimization 71(11):3363–3381, 2022, https://doi.org/10.1080/02331934.2022.2101111 ) to cover the case where the moving set may be nonsmooth. Noteworthy, we consider problems with constrained end point. A remarkable feature of our work is that we rely upon an ingenious smooth approximating family of standard differential equations in the vein of that used in de Pinho et al. (Set Valued Var Anal 27:523–548, 2019, https://doi.org/10.1007/s11228-018-0501-8 ).

Suggested Citation

  • Maria do Rosário de Pinho & Maria Margarida A. Ferreira & Georgi Smirnov, 2023. "A Maximum Principle for Optimal Control Problems Involving Sweeping Processes with a Nonsmooth Set," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 273-297, October.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02283-4
    DOI: 10.1007/s10957-023-02283-4
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    References listed on IDEAS

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    1. MdR Pinho & M. M. A. Ferreira & G. Smirnov, 2020. "Optimal Control with Sweeping Processes: Numerical Method," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 845-858, June.
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