TIME OPTIMAL CONTROL OF THE HEAT EQUATION WITH POINTWISE CONTROL CONSTRAINTS

被引：48

作者：

Kunisch, Karl ^{[1
]}

Wang, Lijuan ^{[2
,3
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math, A-8010 Graz, Austria

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[3] Radon Inst, Linz, Austria

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 02期

基金：

中国国家自然科学基金; 奥地利科学基金会;

关键词：

Bang-bang property; time optimal control; norm optimal control; BANG-BANG PRINCIPLE; APPROXIMATE CONTROLLABILITY; BOUNDARY CONTROL;

D O I：

10.1051/cocv/2012017

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Time optimal control problems for an internally controlled heat equation with point-wise control constraints are studied. By Pontryagin's maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained.

引用

页码：460 / 485

页数：26

共 24 条

[1]

[Anonymous], 1993, MATH SCI ENG

[2]

[Anonymous], JORNADAS HISPANO FRA

[3]

[Anonymous], 2000, THEORY APPL

[4]

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

[5]

[Anonymous], 2004, QUELQUES QUESTIONS T

[6]

[Anonymous], 2006, Elliptic and Parabolic Equations

[7]

[Anonymous], 1964, Applied Mathematics and Optimization

[8]

[Anonymous], CUBO A

[9]

Arada N, 2003, DISCRETE CONT DYN-A, V9, P1549

[10] Dirichlet boundary control of semilinear parabolic equations - Part 1: Problems with no state constraints [J].

Arada, N ;

Raymond, JP .

APPLIED MATHEMATICS AND OPTIMIZATION, 2002, 45 (02) :125-143

← 1 2 3 →