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

Nicolás Espitia (1, 2) , Andrey Polyakov (2) , Denis Efimov (2) , Wilfrid Perruquetti (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 VALSE - Finite-time control and estimation for distributed systems

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.

Mots clés: generalized Laguerre polynomials; fixed-time stabilization; backstepping method; time-varying feedbacks; Linear reaction-diffusion systems

Domaines: Automatique / Robotique

Nicolás Espitia, Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti. Boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems. Automatica, 2019, 103, pp.398-407. ⟨10.1016/j.automatica.2019.02.013⟩. ⟨hal-01962662⟩