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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Detalhes bibliográficos
Autores: Vázquez Valenzuela, Rafael, Krstic, Miroslav
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2016
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/111783
Acesso em linha:https://hdl.handle.net/11441/111783
https://doi.org/10.1109/TAC.2016.2590506
Access Level:Acceso aberto
Palavra-chave:Advection-reaction-diffusion systems
Backstepping
Boundary control
Distributed parameter systems
Parabolic equations
Descrição
Resumo: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.