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Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation
Joint Authors
Zheng, Guojie
Jiang, H.
Ganesan, Arthi
Yu, Xin
Xu, Chao
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-13
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
This paper deals with the stabilization problem of first-order hyperbolic partial differential equations (PDEs) with spatial-temporal actuation over the full physical domains.
We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differential equation (ODE).
A Volterra integral transformation is used to convert the original system into a simple target system using the backstepping-like procedure.
Unlike the classical backstepping techniques for boundary control problems of PDEs, the internal actuation can not eliminate the residual term that causes the instability of the open-loop system.
Thus, an additional differential transformation is introduced to transfer the input from the interior of the domain onto the boundary.
Then, a feedback control law is designed using the classic backstepping technique which can stabilize the first-order hyperbolic PDE system in a finite time, which can be proved by using the semigroup arguments.
The effectiveness of the design is illustrated with some numerical simulations.
American Psychological Association (APA)
Yu, Xin& Xu, Chao& Jiang, H.& Ganesan, Arthi& Zheng, Guojie. 2014. Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1033905
Modern Language Association (MLA)
Yu, Xin…[et al.]. Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation. Abstract and Applied Analysis No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-1033905
American Medical Association (AMA)
Yu, Xin& Xu, Chao& Jiang, H.& Ganesan, Arthi& Zheng, Guojie. Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1033905
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033905