Stabilization of a Chain of Three Hyperbolic PDEs using a Time-Delay Representation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913812706230272 |
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| author | Braun, Adam Auriol, Jean Brivadis, Lucas |
| author_facet | Braun, Adam Auriol, Jean Brivadis, Lucas |
| contents | This paper addresses the stabilization of a chain system consisting of three hyperbolic Partial Differential Equations (PDEs). The system is reformulated into a pure transport system of equations via an invertible backstepping transformation. Using the method of characteristics and exploiting the inherent cascade structure of the chain, the stabilization problem is reduced to that of an associated Integral Difference Equation (IDE). A dynamic controller is designed for the IDE, whose gains are computed by solving a system of Fredholm-type integral equations. This approach provides a systematic framework for achieving exponential stabilization of the chain of hyperbolic PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilization of a Chain of Three Hyperbolic PDEs using a Time-Delay Representation Braun, Adam Auriol, Jean Brivadis, Lucas Optimization and Control This paper addresses the stabilization of a chain system consisting of three hyperbolic Partial Differential Equations (PDEs). The system is reformulated into a pure transport system of equations via an invertible backstepping transformation. Using the method of characteristics and exploiting the inherent cascade structure of the chain, the stabilization problem is reduced to that of an associated Integral Difference Equation (IDE). A dynamic controller is designed for the IDE, whose gains are computed by solving a system of Fredholm-type integral equations. This approach provides a systematic framework for achieving exponential stabilization of the chain of hyperbolic PDEs. |
| title | Stabilization of a Chain of Three Hyperbolic PDEs using a Time-Delay Representation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.10002 |