Sliding mode boundary control for exponential stabilization of linear parabolic distributed parameter systems subject to external disturbance
In this article, we are concerned with the exponential stabilization of parabolic distributed parameter systems with Neumann/mixed boundary conditions and external disturbance. To deal with the bounded disturbance, a sliding mode boundary control scheme is adopted based on the backstepping method. F...
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| Published in | International journal of robust and nonlinear control Vol. 33; no. 15; pp. 9364 - 9390 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Bognor Regis
Wiley Subscription Services, Inc
01.10.2023
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| Abstract | In this article, we are concerned with the exponential stabilization of parabolic distributed parameter systems with Neumann/mixed boundary conditions and external disturbance. To deal with the bounded disturbance, a sliding mode boundary control scheme is adopted based on the backstepping method. Firstly, the exponential stability of the considered system is proven along the selected sliding surface. Secondly, a sliding mode boundary controller is designed to regulate the closed‐loop system trajectory to a suitable sliding surface within a prescribed time and then maintain the sliding motion on the surface. Thirdly, on the chosen sliding surface, the closed‐loop system with the sliding mode boundary controller is exponentially stable. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. |
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| AbstractList | In this article, we are concerned with the exponential stabilization of parabolic distributed parameter systems with Neumann/mixed boundary conditions and external disturbance. To deal with the bounded disturbance, a sliding mode boundary control scheme is adopted based on the backstepping method. Firstly, the exponential stability of the considered system is proven along the selected sliding surface. Secondly, a sliding mode boundary controller is designed to regulate the closed‐loop system trajectory to a suitable sliding surface within a prescribed time and then maintain the sliding motion on the surface. Thirdly, on the chosen sliding surface, the closed‐loop system with the sliding mode boundary controller is exponentially stable. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. |
| Author | Wu, Wei Cui, Baotong Bao, Chunxia Lou, Xuyang Jia, Jiajia |
| Author_xml | – sequence: 1 givenname: Chunxia orcidid: 0000-0001-5906-5851 surname: Bao fullname: Bao, Chunxia organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education) and School of IoT Engineering Jiangnan University Wuxi China – sequence: 2 givenname: Baotong surname: Cui fullname: Cui, Baotong organization: College of Mathematics and Physics Inner Mongolia Minzu University Tongliao China – sequence: 3 givenname: Xuyang surname: Lou fullname: Lou, Xuyang organization: College of Mathematics and Physics Inner Mongolia Minzu University Tongliao China – sequence: 4 givenname: Wei surname: Wu fullname: Wu, Wei organization: College of Mathematics and Physics Inner Mongolia Minzu University Tongliao China – sequence: 5 givenname: Jiajia surname: Jia fullname: Jia, Jiajia organization: College of Mathematics and Physics Inner Mongolia Minzu University Tongliao China |
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| SubjectTerms | Boundary conditions Boundary control Control systems design Controllers Distributed parameter systems Sliding mode control Stabilization |
| Title | Sliding mode boundary control for exponential stabilization of linear parabolic distributed parameter systems subject to external disturbance |
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