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

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...

Descripción completa

Detalles Bibliográficos
Autores: Vázquez Valenzuela, Rafael, Krstic, Miroslav
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/69757
Acceso en línea:https://hdl.handle.net/11441/69757
https://doi.org/10.1051/cocv/2016033
Access Level:acceso abierto
Palabra clave:Infinite-dimensional backstepping
Boundary control
Boundary observer
Descripción
Sumario: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.