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Communication Dans Un Congrès Année : 2020

Backstepping control for a class of coupled hyperbolic-parabolic PDE systems

Mohammad Ghousein
Emmanuel Witrant

Résumé

In this work, we consider the boundary stabilization of a linear diffusion equation coupled with a linear transport equation. This type of hyperbolic-parabolic partial differential equations (PDEs) coupling arises in many biological, chemical and thermal systems. The two equations are coupled inside the domain and at the boundary. The in-domain coupling architecture is considered from both sides i.e. an advection source term driven by the transport PDE and a Volterra integral source term driven by the parabolic PDE. Using a backstepping method, we derive two feedback control laws and we give sufficient conditions for the exponential stability of the coupled system in the L 2 norm. Controller gains are calculated by solving hyperbolic-parabolic kernel equations arising from the backstepping transformations. The theoretical results are illustrated by numerical simulations.
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Dates et versions

hal-03107240 , version 1 (12-01-2021)

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Mohammad Ghousein, Emmanuel Witrant. Backstepping control for a class of coupled hyperbolic-parabolic PDE systems. ACC 2020 - American Control Conference, Jul 2020, Denver (online), United States. pp.1600-1605, ⟨10.23919/ACC45564.2020.9147593⟩. ⟨hal-03107240⟩
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