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Mathematics 2019, 7(4), 311; https://doi.org/10.3390/math7040311

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

1
School of Mathematics and Statics, Guizhou University, Guiyang 550025, China
2
School of Mathematics Science, Zunyi Normal University, Zunyi 563006, China
3
School of Mathematics, Guizhou Minzu University, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
Received: 27 February 2019 / Revised: 18 March 2019 / Accepted: 21 March 2019 / Published: 28 March 2019
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PDF [761 KB, uploaded 28 March 2019]

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. View Full-Text
Keywords: Petrowsky system; time-optimal control; null-controllability; existence of time-optimal control; bang-bang property Petrowsky system; time-optimal control; null-controllability; existence of time-optimal control; bang-bang property
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Luo, D.; Wei, W.; Deng, H.; Liao, Y. The Time-Optimal Control Problem of a Kind of Petrowsky System. Mathematics 2019, 7, 311.

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