Repositorio de producción científica de la Universidad de Sevilla

Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls

 

Advanced Search
 
Opened Access Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls
Cites

Show item statistics
Icon
Export to
Author: Vázquez Valenzuela, Rafael
Krstic, Miroslav
Department: Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos
Date: 2016
Published in: ESAIM: Control, Optimisation and Calculus of Variations, 22 (4), 1078-1096.
Document type: Article
Abstract: This paper introduces an explicit output-feedback boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an n-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 L2 and H1 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 n-ball.
Cite: Vázquez Valenzuela, R. y Krstic, M. (2016). Explicit output-feedback boundary control of reaction-diffusion PDEs on arbitrary-dimensional balls. ESAIM: Control, Optimisation and Calculus of Variations, 22 (4), 1078-1096.
Size: 234.2Kb
Format: PDF

URI: https://hdl.handle.net/11441/69757

DOI: 10.1051/cocv/2016033

See editor´s version

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)