This paper introduces an explicit output-feedback boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an -ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere) using only measurements from the boundary. The backstepping method is used to design both the control law and a boundary observer. To apply backstepping the system is reduced to an infinite sequence of 1-D systems using spherical harmonics. Well-posedness and stability are proved in the and spaces. The resulting control and output injection gain kernels are the product of the backstepping kernel used in control of one-dimensional reaction-diffusion equations and a function closely related to the Poisson kernel in the -ball.
Accepté le :
DOI : 10.1051/cocv/2016033
Mots-clés : Infinite-dimensional backstepping, boundary control, boundary observer, reaction-diffusion system, spherical harmonics
@article{COCV_2016__22_4_1078_0,
author = {Vazquez, Rafael and Krstic, Miroslav},
title = {Explicit output-feedback boundary control of reaction-diffusion {PDEs} on arbitrary-dimensional balls},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1078--1096},
publisher = {EDP-Sciences},
volume = {22},
number = {4},
year = {2016},
doi = {10.1051/cocv/2016033},
mrnumber = {3570495},
zbl = {1358.35058},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2016033/}
}
TY - JOUR AU - Vazquez, Rafael AU - Krstic, Miroslav TI - Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 1078 EP - 1096 VL - 22 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2016033/ DO - 10.1051/cocv/2016033 LA - en ID - COCV_2016__22_4_1078_0 ER -
%0 Journal Article %A Vazquez, Rafael %A Krstic, Miroslav %T Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 1078-1096 %V 22 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2016033/ %R 10.1051/cocv/2016033 %G en %F COCV_2016__22_4_1078_0
Vazquez, Rafael; Krstic, Miroslav. Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1078-1096. doi : 10.1051/cocv/2016033. http://www.numdam.org/articles/10.1051/cocv/2016033/
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