Time-varying bang-bang property of time optimal controls for heat equation and its application

被引：17

作者：

Chen, Ning ^{[1
]}

Wang, Yanqing ^{[2
]}

Yang, Dong-Hui ^{[1
,3
]}

机构：

[1] Cent S Univ, Sch Informat Sci & Engn, Changsha 410075, Hunan, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[3] Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China

来源：

SYSTEMS & CONTROL LETTERS | 2018年 / 112卷

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Heat equation; Bang-bang property; Time optimal control problem; Target optimal control problem; NULL CONTROLLABILITY; BOUNDARY CONTROL; PRINCIPLE; EQUIVALENCE;

D O I：

10.1016/j.sysconle.2017.12.008

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, the bang-bang property of time optimal controls for heat equation is established. Compared with the existing results on these problems, the bound of control variables is not a constant but a time-varying function. As an application of the bang-bang property, some kind of relation between the time optimal control problem and its corresponding target optimal control problem is considered. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：18 / 23

页数：6

共 30 条

[1]

[Anonymous], 1999, APPL MATH

[2]

[Anonymous], 1956, Quarterly of Applied Mathematics, DOI DOI 10.1090/QAM/78516

[3] Observability inequalities and measurable sets [J].

Apraiz, J. ;

Escauriaza, L. ;

Wang, G. ;

Zhang, C. .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2014, 16 (11) :2433-2475

[4]

Faber C., 1995, P ROY SOC EDINB A, V125, P31

[5] TIME AND NORM OPTIMAL CONTROLS: A SURVEY OF RECENT RESULTS AND OPEN PROBLEMS [J].

Fattorini, H. O. .

ACTA MATHEMATICA SCIENTIA, 2011, 31 (06) :2203-2218

[6]

Fattorini H.O., 1999, Encyclopedia of Mathematics and its Applications, V62

[7] Null and approximate controllability for weakly blowing up semilinear heat equations [J].

Fernández-Cara, E ;

Zuazua, E .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2000, 17 (05) :583-616

[8]

Fuisikov A. V., 1996, CONTROLLABILITY EVOL

[9] Regularity of the minimum time function and minimum energy problems: The linear case [J].

Gozzi, F ;

Loreti, P .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (04) :1195-1221

[10] Optimal actuator location of minimum norm controls for heat equation with general controlled domain [J].

Guo, Bao-Zhu ;

Xu, Yashan ;

Yang, Dong-Hui .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (06) :3588-3614

← 1 2 3 →