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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.19073 |
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| _version_ | 1866909775245082624 |
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| author | Zhang, Chuan Yang, He Wang, Fei Zhou, Tuo |
| author_facet | Zhang, Chuan Yang, He Wang, Fei Zhou, Tuo |
| contents | This paper presents a boundary control scheme for prescribed-time (PT) stable of flexible string systems via backstepping method, and the dynamics of such systems modeled by Hamilton's principle is described as second-order hyperbolic partial differential equations (PDEs). Initially, to construct a boundary controller with PT stabilization capacity, a PT stable hyperbolic PDEs system with time-varying coefficient is chosen as the target system, and a corresponding Volterra integral transform with time-varying kernel function is considered. Then, to identify the boundary controller, the well-posedness of kernel equation is derived by means of successive approximation and mathematical induction, and the upper bound of kernel function is estimated. Furthermore, the inverse transform is proved with the help of a similar process for kernel function. Subsequently, the PT stability of closed-loop system is proved by PT stability of target system and reversible integral transform. Finally, the simulation results demonstrate the effectiveness of our scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prescribed-time boundary control of second-order hyperbolic PDEs modeled flexible string systems via backstepping design Zhang, Chuan Yang, He Wang, Fei Zhou, Tuo Optimization and Control Analysis of PDEs This paper presents a boundary control scheme for prescribed-time (PT) stable of flexible string systems via backstepping method, and the dynamics of such systems modeled by Hamilton's principle is described as second-order hyperbolic partial differential equations (PDEs). Initially, to construct a boundary controller with PT stabilization capacity, a PT stable hyperbolic PDEs system with time-varying coefficient is chosen as the target system, and a corresponding Volterra integral transform with time-varying kernel function is considered. Then, to identify the boundary controller, the well-posedness of kernel equation is derived by means of successive approximation and mathematical induction, and the upper bound of kernel function is estimated. Furthermore, the inverse transform is proved with the help of a similar process for kernel function. Subsequently, the PT stability of closed-loop system is proved by PT stability of target system and reversible integral transform. Finally, the simulation results demonstrate the effectiveness of our scheme. |
| title | Prescribed-time boundary control of second-order hyperbolic PDEs modeled flexible string systems via backstepping design |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2412.19073 |