Journal
IET CONTROL THEORY AND APPLICATIONS
Volume 10, Issue 11, Pages 1250-1257Publisher
INST ENGINEERING TECHNOLOGY-IET
DOI: 10.1049/iet-cta.2015.0882
Keywords
reaction-diffusion systems; partial differential equations; linear systems; stability; sensors; actuators; closed loop systems; feedback; reaction-diffusion process; sensor pairs; one-dimensional domain; actuator pairs; collocated pairs; anti-collocated pairs; closed-loop solutions; linear hyperbolic PDE; Mittag-Leffler stability linear system; invertible coordinate transformation; Caputo time fractional derivative; normal reaction-diffusion equation; first-order time derivative; fractional-order partial differential equation; unstable heat process; time fractional-order anomalous diffusion system; boundary feedback stabilisation
Categories
Funding
- Chinese Universities Scientific Fund [CUSF-DH-D-2014061]
- Natural Science Foundation of Shanghai [15ZR1400800]
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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 (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.
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