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Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications

Author

Listed:
  • Emilio Molina

    (Universidad de Chile
    Sorbonne Université
    CaGe, INRIA)

  • Alain Rapaport

    (Université Montpellier)

  • Héctor Ramírez

    (Universidad de Chile)

Abstract

We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples.

Suggested Citation

  • Emilio Molina & Alain Rapaport & Héctor Ramírez, 2022. "Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 953-975, December.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:3:d:10.1007_s10957-022-02094-z
    DOI: 10.1007/s10957-022-02094-z
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    References listed on IDEAS

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    1. S. C. Di Marco & R. L. V. González, 1999. "Relaxation of Minimax Optimal Control Problems with Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 285-306, May.
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