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Minimal Norm Control Problem Governed by Semilinear Heat Equation with Impulse Control

Author

Listed:
  • Yueliang Duan

    (Wuhan University)

  • Lijuan Wang

    (Wuhan University)

Abstract

This paper studies a kind of minimal norm optimal control problem for a semilinear heat equation with impulse controls; it consists in finding an impulse control, which has the minimal norm among all controls steering solutions of the controlled system to a given target from an initial state in a fixed time interval. We will study the existence of optimal controls to this problem. Then, we will establish a nontrivial Pontryagin’s maximum principle of this problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01594-9
    DOI: 10.1007/s10957-019-01594-9
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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. G. Wang & L. Wang, 2003. "The Carleman Inequality and Its Application to Periodic Optimal Control Governed by Semilinear Parabolic Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 429-461, August.
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    Cited by:

    1. 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.

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