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Minimal Time Impulse Control Problem of Semilinear Heat Equation

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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.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under Grant 11771344.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, China

    Lijuan Wang

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  1. Lijuan Wang
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Correspondence to Lijuan Wang.

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Communicated by Michael Hinze.

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Wang, L. Minimal Time Impulse Control Problem of Semilinear Heat Equation. J Optim Theory Appl 188, 805–822 (2021). https://doi.org/10.1007/s10957-020-01807-6

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  • DOI: https://doi.org/10.1007/s10957-020-01807-6

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