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

被引：0

作者：

Luo, Dongsheng ^{[1
,2
]}

Wei, Wei ^{[1
,3
]}

Deng, Hongyong ^{[3
]}

Liao, Yumei ^{[1
]}

机构：

[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China

[2] Zunyi Normal Univ, Sch Math Sci, Zunyi 563006, Peoples R China

[3] Guizhou Minzu Univ, Sch Math, Guiyang 550025, Guizhou, Peoples R China

来源：

MATHEMATICS | 2019年 / 7卷 / 04期

关键词：

Petrowsky system; time-optimal control; null-controllability; existence of time-optimal control; bang-bang property; 49K15; 49K30; 35B35; 93B07; BANG-BANG PROPERTY; VIBRATION CONTROL; BEAM; PLATES; MASS;

D O I：

10.3390/math7040311

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：12

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