Abstract
In this paper, we consider bang–bang property for a kind of time-varying time optimal control problem of null controllable heat equation. The study is a continuation of a recent work (Chen et al. in Syst Control Lett 112:18–23, 2018), where an approximate null controllable heat equation was considered. We first establish the equivalence between optimal norm control and optimal time control and then prove the existence of the optimal norm control and of the optimal time control. The time-varying bang–bang property for the optimal time control is finally established.
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Acknowledgements
The authors would like to thank Dr. Yubiao Zhang of Tianjin University for his helpful discussion during preparation of this work. The authors are grateful to editor for many useful comments on presentation. The constructive suggestions from anonymous referees are very helpful to improve the manuscript substantially. This work was carried out with the supports of the National Natural Science Foundation of China and the Project of Department of Education of Guangdong Province (No. 2017KZDXM087).
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Communicated by Enrique Zuazua.
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Yang, DH., Guo, BZ., Gui, W. et al. The Bang–Bang Property of Time-Varying Optimal Time Control for Null Controllable Heat Equation. J Optim Theory Appl 182, 588–605 (2019). https://doi.org/10.1007/s10957-019-01510-1
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DOI: https://doi.org/10.1007/s10957-019-01510-1