Open AccessBoundary feedback stabilisation for the time fractional‐order anomalous diffusion system
Author(s) -
Ge Fudong,
Chen YangQuan,
Kou Chunhai
Publication year - 2016
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.2015.0882
Subject(s) - invertible matrix , fractional calculus , mathematics , boundary (topology) , partial differential equation , transformation (genetics) , stability (learning theory) , control theory (sociology) , coordinate system , domain (mathematical analysis) , actuator , mathematical analysis , partial derivative , boundary value problem , computer science , geometry , control (management) , artificial intelligence , biochemistry , chemistry , machine learning , pure mathematics , gene
In this study, the authors attempt to explore the boundary feedback stabilisation for an unstable heat process described by fractional‐order partial differential equation (PDE), where the first‐order time derivative of normal reaction–diffusion equation is replaced by a Caputo time fractional derivative of order α∈(0, 1]. By designing an invertible coordinate transformation, the system under consideration is converted into a Mittag–Leffler stability linear system and the boundary stabilisation problem is transformed into a problem of solving a linear hyperbolic PDE. It is worth mentioning that with the help of this invertible coordinate transformation, they can explicitly obtain the closed‐loop solutions of the original problem. The output feedback problem with both anti‐collocated and collocated actuator/sensor pairs in one‐dimensional domain is also presented. A numerical example is given to test the effectiveness of the authors' results.