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
收藏
页数：12
相关论文
共 50 条
  • [1] On a kind of time optimal control problem of the heat equation
    Zhang, Yifan
    ADVANCES IN DIFFERENCE EQUATIONS, 2018,
  • [2] Bang-Bang Property of Time Optimal Control for a Kind of Microwave Heating Problem
    Luo, Dongsheng
    Wei, Wei
    Liao, Yumei
    Deng, Hongyong
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2019, 183 (01) : 317 - 331
  • [3] A New Approach to a Fuzzy Time-Optimal Control Problem
    Amrahov, S. Emrah
    Gasilov, N. A.
    Fatullayev, A. G.
    CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2014, 99 (05): : 351 - 369
  • [4] Time-Optimal Control Problem in the Space of Probability Measures
    Cavagnari, Giulia
    Marigonda, Antonio
    LARGE-SCALE SCIENTIFIC COMPUTING, LSSC 2015, 2015, 9374 : 109 - 116
  • [5] Time-optimal control of a particle in a dielectrophoretic system
    Chang, Dong Eui
    Petit, Nicolas
    Rouchon, Pierre
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (07) : 1100 - 1114
  • [6] Asymptotic Method for Solving the Time-Optimal Control Problem for a Nonlinear Singularly Perturbed System
    Grudo, Ya. O.
    Kalinin, A. I.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2008, 48 (11) : 1945 - 1954
  • [7] Asymptotic method for solving the time-optimal control problem for a nonlinear singularly perturbed system
    Ya. O. Grudo
    A. I. Kalinin
    Computational Mathematics and Mathematical Physics, 2008, 48 : 1945 - 1954
  • [8] 'Transportation' problem of time-optimal heating
    Pleshivtseva, Yulia
    INTERNATIONAL JOURNAL OF MATERIALS & PRODUCT TECHNOLOGY, 2007, 29 (1-4): : 137 - 148
  • [9] AVERAGED TIME-OPTIMAL CONTROL PROBLEM IN THE SPACE OF POSITIVE BOREL MEASURES
    Cavagnari, Giulia
    Marigonda, Antonio
    Piccoli, Benedetto
    ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2018, 24 (02) : 721 - 740
  • [10] REGULARITY RESULTS FOR A TIME-OPTIMAL CONTROL PROBLEM IN THE SPACE OF PROBABILITY MEASURES
    Cavagnari, Giulia
    MATHEMATICAL CONTROL AND RELATED FIELDS, 2017, 7 (02) : 213 - 233
12345