Open AccessObserver‐based output feedback control for a boundary controlled fractional reaction diffusion system with spatially‐varying diffusivity
Author(s) -
Chen Juan,
Cui Baotong,
Chen Yang Quan
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.1352
Subject(s) - control theory (sociology) , backstepping , observer (physics) , boundary (topology) , controller (irrigation) , mathematics , computer science , control (management) , mathematical analysis , adaptive control , physics , artificial intelligence , quantum mechanics , agronomy , biology
This study is concerned with observer design and observer‐based output feedback control for a fractional reaction diffusion (FRD) system with a spatially‐varying (non‐constant) diffusion coefficient by the backstepping method. The considered FRD system is endowed with only boundary measurable and actuation available. The contribution of this study is divided into three parts: first is the backstepping‐based observer design for the FRD system with non‐constant diffusivity, second is the output feedback controller generated by the integration of a separately backstepping‐based feedback controller and the proposed observer to stabilise the FRD system with non‐constant diffusivity, and the last is the Mittag–Leffler stability analysis of the observer error and the closed‐loop FRD systems. Specifically, anti‐collocated location of actuator and sensor is considered in the stabilisation problem of this system with Robin boundary condition at x = 0 and the boundary feedback controller for Dirichlet actuation at x = 1 . By designing an invertible coordinate transformation to convert the observer error system into a Mittag–Leffler stable target system, the observer gains are obtained. They are used to design the output feedback control law for stabilising the closed‐loop system. Finally, a numerical example is shown to validate the effectiveness of the authors' proposed method.