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2014 Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation
Xin Yu, Chao Xu, Huacheng Jiang, Arthi Ganesan, Guojie Zheng
Abstr. Appl. Anal. 2014: 1-13 (2014). DOI: 10.1155/2014/643640


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.


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Xin Yu. Chao Xu. Huacheng Jiang. Arthi Ganesan. Guojie Zheng. "Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation." Abstr. Appl. Anal. 2014 1 - 13, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022812
MathSciNet: MR3251533
Digital Object Identifier: 10.1155/2014/643640

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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