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

Dongsheng Luo, Wei Wei, Hongyong Deng and Yumei Liao
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Dongsheng Luo: School of Mathematics and Statics, Guizhou University, Guiyang 550025, China
Wei Wei: School of Mathematics and Statics, Guizhou 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

Mathematics, 2019, vol. 7, issue 4, 1-12

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.

Keywords: Petrowsky system; time-optimal control; null-controllability; existence of time-optimal control; bang-bang property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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