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Minimal Time Impulse Control Problem of Semilinear Heat Equation

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  • Lijuan Wang

    (Wuhan University)

Abstract

The paper is concerned with a kind of minimal time impulse control problem for a semilinear heat equation. We study the existence of optimal controls of this problem, establish a nontrivial Pontryagin’s maximum principle for this problem and then derive the bang–bang property of optimal controls. Based on the existence and the bang–bang property of optimal controls, we discuss the equivalence of the minimal time impulse control problem and its corresponding minimal norm impulse control problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:3:d:10.1007_s10957-020-01807-6
    DOI: 10.1007/s10957-020-01807-6
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    References listed on IDEAS

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    1. Yueliang Duan & Lijuan Wang & Can Zhang, 2019. "Minimal Time Impulse Control of an Evolution Equation," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 902-919, December.
    2. Yueliang Duan & Lijuan Wang, 2020. "Minimal Norm Control Problem Governed by Semilinear Heat Equation with Impulse Control," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 400-418, February.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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