Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation
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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/643640 |
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| author | Xin Yu Chao Xu Huacheng Jiang Arthi Ganesan Guojie Zheng |
| author_facet | Xin Yu Chao Xu Huacheng Jiang Arthi Ganesan Guojie Zheng |
| author_sort | Xin Yu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b615f2eaa40b49bd8008df81007f1e5b |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b615f2eaa40b49bd8008df81007f1e5b2025-08-20T03:20:55ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/643640643640Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal ActuationXin Yu0Chao Xu1Huacheng Jiang2Arthi Ganesan3Guojie Zheng4Laboratory of Information & Control Technology, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, ChinaThe State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mathematics, Zhejiang University, Hangzhou 310027, ChinaThe State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou 310027, ChinaCollege of Mathematics & Information Science, Henan Normal University, Xinxiang 453007, ChinaThis 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.http://dx.doi.org/10.1155/2014/643640 |
| spellingShingle | Xin Yu Chao Xu Huacheng Jiang Arthi Ganesan Guojie Zheng Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation Abstract and Applied Analysis |
| title | Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation |
| title_full | Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation |
| title_fullStr | Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation |
| title_full_unstemmed | Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation |
| title_short | Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation |
| title_sort | backstepping synthesis for feedback control of first order hyperbolic pdes with spatial temporal actuation |
| url | http://dx.doi.org/10.1155/2014/643640 |
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