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access icon free Backstepping-based boundary feedback control for a fractional reaction diffusion system with mixed or Robin boundary conditions

  • Author(s): Juan Chen 1 ; Bo Zhuang 1 ; YangQuan Chen 2 ; Baotong Cui 1
    • View affiliations
  • Source: Volume 11, Issue 17, 24 November 2017, p. 2964 – 2976
    DOI:  10.1049/iet-cta.2017.0227 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 26/02/2017, Accepted 22/08/2017, Revised 26/07/2017, Published 23/08/2017

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.

Inspec keywords: Lyapunov methods; distributed parameter systems; open loop systems; stability; feedback; reaction-diffusion systems; closed loop systems; control nonlinearities

Other keywords: fractional reaction diffusion system; stabilisation problem; Robin backstepping-based boundary feedback controllers; Dirichlet backstepping-based boundary feedback controller; closed-loop solutions; open-loop solutions; FRD system; Lyapunov-based Mittag-Leffler stability theory; Robin boundary conditions; Neumann backstepping-based boundary feedback controllers

Subjects: Nonlinear control systems; Distributed parameter control systems; Stability in control theory

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