Some characterizations of boundary time-varying feedbacks for fixed-time stabilization of reaction-diffusion systems. Issue 2 (2019)

• Record Type: Journal Article
• Authors: Espitia, Nicolás; Polyakov, Andrey; Efimov, Denis; Perruquetti, Wilfrid
• Is Part Of: IFAC-PapersOnLine. Volume 52:Issue 2(2019)
• Page Start: 162
• Page End: 167
• Publication Date: 2019
• Subjects: Reaction-diffusion equations -- time-varying feedbacks -- fixed-time convergence -- exponential Bell polynomials -- generalized Laguerre polynomials; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2019.08.029
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper deals with continuous boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems. The time of convergence can be prescribed and is independent of the initial condition of the system. The design of time-varying feedbacks is carried out by using the backstepping approach for which suitable characterizations for time-varying kernels are derived. Kernel solutions are given in terms of power series involving the exponential complete Bell polynomials for which we have exploited the Fa à di Bruno formula . Moreover, by particularizing the characterization, one can recover kernel solutions in terms of the generalized Laguerre polynomials and the modified Bessel functions .