We consider the problem of boundary stabilization for a system of n coupled parabolic linear PDEs of the reaction-diffusion-advection type. Particularly, we design a state-feedback law with Dirichlet-type actuation on only one end of the domain and prove exponential stability of the closed-loop system with an arbitrarily fast convergence rate. The backstepping method is used for controller design, and the transformation kernel matrix is derived by using the method of successive approximations to solve the corresponding PDE. Simulation results support the effectiveness of the suggested design.

Boundary control of coupled reaction-advection-diffusion equations having the same diffusivity parameter

Pisano, Alessandro;Baccoli, Antonello;Usai, Elio
2016

Abstract

We consider the problem of boundary stabilization for a system of n coupled parabolic linear PDEs of the reaction-diffusion-advection type. Particularly, we design a state-feedback law with Dirichlet-type actuation on only one end of the domain and prove exponential stability of the closed-loop system with an arbitrarily fast convergence rate. The backstepping method is used for controller design, and the transformation kernel matrix is derived by using the method of successive approximations to solve the corresponding PDE. Simulation results support the effectiveness of the suggested design.
Backstepping; Boundary control; Distributed-parameter systems; Reaction-advection-diffusion equation; Control and systems engineering
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/236155
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