Stabilization and controllability of first-order integro-differential hyperbolic equations

被引：34

作者：

Coron, Jean-Michel ^{[1
]}

Hu, Long ^{[1
,2
]}

Olive, Guillaume ^{[1
]}

机构：

[1] UPMC Univ Paris 06, Sorbonne Univ, UMR 7598, Lab Jacques Louis Lions, 4 Pl Jussieu, F-75252 Paris 05, France

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2016年 / 271卷 / 12期

关键词：

Integro-differential equation; Stabilization; Controllability; Fredholm backstepping; transformation; DIMENSIONAL INPUT OPERATORS; SYSTEMS; STABILIZABILITY; PDES;

D O I：

10.1016/j.jfa.2016.08.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present article we study the stabilization of first order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prove the invertibility of such a transformation. Finally, using the method of moments, we show in a particular rase that the controllability is reduced to the criterion of Fattorini. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：3554 / 3587

页数：34

共 22 条

[1] ON THE FATTORINI CRITERION FOR APPROXIMATE CONTROLLABILITY AND STABILIZABILITY OF PARABOLIC SYSTEMS [J].

Badra, Mehdi ;

Takahashi, Takeo .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2014, 20 (03) :924-956

[2] Backstepping in infinite dimension for a class of parabolic distributed parameter systems [J].

Boskovic, DM ;

Balogh, A ;

Krstic, M .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2003, 16 (01) :44-75

[3] Backstepping-Forwarding Control and Observation for Hyperbolic PDEs With Fredholm Integrals [J].

Bribiesca-Argomedo, Federico ;

Krstic, Miroslav .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2015, 60 (08) :2145-2160

[4]

Coron J.-M., 2007, MATH SURVEYS MONOGR, V136

[5] Fredholm transform and local rapid stabilization for a Kuramoto-Sivashinsky equation [J].

Coron, Jean-Michel ;

Lu, Qi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (08) :3683-3729

[6] Local rapid stabilization for a Korteweg-de Vries equation with a Neumann boundary control on the right [J].

Coron, Jean-Michel ;

Lu, Qi .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2014, 102 (06) :1080-1120

[7]

Fattorini HO., 1966, SIAM J. Control, V4, P686, DOI [10.1137/0304048, DOI 10.1137/0304048]

[8] Riesz bases and exact controllability of C0-groups with one-dimensional input operators [J].

Guo, BZ ;

Xu, GQ .

SYSTEMS & CONTROL LETTERS, 2004, 52 (3-4) :221-232

[9]

HAUTUS MLJ, 1969, P K NED AKAD A MATH, V72, P443

[10]

HOCHSTADT H, 1973, PURE APPL MATH

← 1 2 3 →