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The Time-Optimal Control Problem of a Kind of Petrowsky System

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  • Dongsheng Luo

    (School of Mathematics and Statics, Guizhou University, Guiyang 550025, China
    School of Mathematics Science, Zunyi Normal University, Zunyi 563006, China)

  • Wei Wei

    (School of Mathematics and Statics, Guizhou University, Guiyang 550025, China
    School of Mathematics, Guizhou Minzu University, Guiyang 550025, China)

  • Hongyong Deng

    (School of Mathematics, Guizhou Minzu University, Guiyang 550025, China)

  • Yumei Liao

    (School of Mathematics and Statics, Guizhou University, Guiyang 550025, China)

Abstract

In this paper, we consider the time-optimal control problem about a kind of Petrowsky system and its bang-bang property. To solve this problem, we first construct another control problem, whose null controllability is equivalent to the controllability of the time-optimal control problem of the Petrowsky system, and give the necessary condition for the null controllability. Then we show the existence of time-optimal control of the Petrowsky system through minimum sequences, for the null controllability of the constructed control problem is equivalent to the controllability of the time-optimal control of the Petrowsky system. At last, with the null controllability, we obtain the bang-bang property of the time-optimal control of the Petrowsky system by contradiction, moreover, we know the time-optimal control acts on one subset of the boundary of the vibration system.

Suggested Citation

  • Dongsheng Luo & Wei Wei & Hongyong Deng & Yumei Liao, 2019. "The Time-Optimal Control Problem of a Kind of Petrowsky System," Mathematics, MDPI, vol. 7(4), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:311-:d:217779
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