Backstepping‐based boundary feedback control for a fractional reaction diffusion system with mixed or Robin boundary conditions

Abstract

This study is concerned with a stabilisation problem of a boundary controlled fractional reaction diffusion (FRD) system with mixed or Robin boundary conditions. The contribution of this study is to utilise boundary feedback control to stabilise the FRD system with mixed or Robin boundary conditions in terms of the backstepping method. Specifically, three backstepping-based boundary feedback controllers have been proposed to address the stabilisation problem of the FRD system with mixed or Robin boundary conditions, including Dirichlet, Neumann, and Robin backstepping-based boundary feedback controllers. Moreover, based on Lyapunov-based Mittag–Leffler stability theory, we prove that the FRD system with mixed or Robin boundary conditions is Mittag–Leffler stable by the proposed three backstepping-based boundary feedback controllers. Finally, the numerical efforts of the open-loop and the closed-loop solutions of the FRD systems with mixed or Robin boundary conditions are presented by two numerical experiments to verify the validness of our results.