Boundary feedback stabilisation for the time fractional‐order anomalous diffusion system. Issue 11 (1st July 2016)

• Record Type: Journal Article
• Authors: Ge, Fudong; Chen, YangQuan; Kou, Chunhai
• Is Part Of: IET control theory & applications. Volume 10:Issue 11(2016)
• Page Start: 1250
• Page End: 1257
• Publication Date: 2016-07-01
• Subjects: 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; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2015.0882
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : 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.