Boundary Control of Coupled Reaction-Advection-Diffusion Systems with Spatially-Varying Coefficients

Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and spatially-varying coefficients is challenging due to complex bo...

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Detalles Bibliográficos
Autores: Vázquez Valenzuela, Rafael, Krstic, Miroslav
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
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:11441/111783
Acceso en línea:https://hdl.handle.net/11441/111783
https://doi.org/10.1109/TAC.2016.2590506
Access Level:acceso abierto
Palabra clave:Advection-reaction-diffusion systems
Backstepping
Boundary control
Distributed parameter systems
Parabolic equations
Descripción
Sumario:Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and spatially-varying coefficients is challenging due to complex boundary conditions that appear in the equations verified by the control kernels. In this technical note we address this issue by showing that these equations are essentially equivalent to those verified by the control kernels for first-order hyperbolic coupled systems, which were recently found to be well-posed. The result therefore applies in this case, allowing us to prove H 1 stability for the closed-loop system. It also unveils a previously unknown connection between backstepping kernels for coupled parabolic and hyperbolic problems.