Title :

Boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems

Author(s) :

Espitia, Nicolas [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Finite-time control and estimation for distributed systems [VALSE]
Polyakov, Andrey [Auteur]
Finite-time control and estimation for distributed systems [VALSE]
Efimov, Denis [Auteur]
Finite-time control and estimation for distributed systems [VALSE]
Perruquetti, Wilfrid [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]

Journal title :

Automatica

Pages :

398-407

Publisher :

Elsevier

Publication date :

2019-05-01

ISSN :

0005-1098

English keyword(s) :

generalized Laguerre polynomials
fixed-time stabilization
backstepping method
time-varying feedbacks
Linear reaction-diffusion systems

HAL domain(s) :

Sciences de l'ingénieur [physics]/Automatique / Robotique

English abstract : [en]

In this paper, the problem of fixed-time stabilization of constant-parameter reaction-diffusion partial differential equations by means of continuous boundary time-varying feedbacks is considered. Moreover, the time of ...
Show more >In this paper, the problem of fixed-time stabilization of constant-parameter reaction-diffusion partial differential equations by means of continuous boundary time-varying feedbacks is considered. Moreover, the time of convergence can be prescribed in the design. The design of time-varying feedbacks is carried out based on the backstepping approach. Using a suitable target system with a time varying-coefficient, one can state that the resulting kernel of the backstepping transformation is time-varying and rendering the control feedback to be time-varying as well. Explicit representations of the kernel solution in terms of generalized Laguerre polynomials and modified Bessel functions are derived. The fixed-time stability property is then proved. A simulation example is presented to illustrate the main results.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL