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Article Dans Une Revue European Journal of Control Année : 2023

Lyapunov-based nonlinear boundary control design with predefined convergence for a class of 1D linear reaction-diffusion equations

Salim Zekraoui
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Nicolás Espitia
Wilfrid Perruquetti

Résumé

In this paper, we treat the problem of Lyapunovbased nonlinear boundary stabilization of a class of onedimensional reaction-diffusion systems with any predefined convergence (asymptotic or non-asymptotic). As an application, we focus on the non-asymptotic notions (finite-time and fixedtime) for which we give some particular explicit control designs followed by some numerical simulations. The key idea of our approach is to use a "spatially weighted L 2-norm" as a Lyapunov functional to design a nonlinear controller and to ensure stability with any desired convergence.

Domaines

Automatique
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Dates et versions

hal-04281668 , version 1 (13-11-2023)

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  • HAL Id : hal-04281668 , version 1

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Salim Zekraoui, Nicolás Espitia, Wilfrid Perruquetti. Lyapunov-based nonlinear boundary control design with predefined convergence for a class of 1D linear reaction-diffusion equations. European Journal of Control, 2023, 74. ⟨hal-04281668⟩
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