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Pontryagin's Principle for Time-Optimal Problems

Author

Listed:
  • J. P. Raymond

    (Université Paul Sabatier, UMR CNRS MIP)

  • H. Zidani

    (Université Paul Sabatier, UMR CNRS MIP)

Abstract

We consider time-optimal control problems for semilinear parabolic equations with pointwise state constraints and unbounded controls. A Pontryagin's principle is obtained in nonqualified form without any qualification condition. The terminal time, which is a control variable, satisfies an optimality condition, which seems to be new in the context of control problems for partial differential equations.

Suggested Citation

  • J. P. Raymond & H. Zidani, 1999. "Pontryagin's Principle for Time-Optimal Problems," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 375-402, May.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:2:d:10.1023_a:1021793611520
    DOI: 10.1023/A:1021793611520
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    Cited by:

    1. B. T. Kien & A. Rösch & D. Wachsmuth, 2017. "Pontryagin’s Principle for Optimal Control Problem Governed by 3D Navier–Stokes Equations," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 30-55, April.
    2. Lijuan Wang, 2021. "Minimal Time Impulse Control Problem of Semilinear Heat Equation," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 805-822, March.
    3. Lijuan Wang & Qishu Yan, 2015. "Time Optimal Controls of Semilinear Heat Equation with Switching Control," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 263-278, April.
    4. B. T. Kien & V. H. Nhu & A. Rösch, 2015. "Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 30-61, April.

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