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

• Autores: Nicolás Espitia, Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 103, 2019, págs. 398-407
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.