Backstepping Control of First-Order Hyperbolic Equations in Arbitrary Dimensions with Non-Trapping Characteristics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916044412551168 |
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| author | Belhadjoudja, Mohamed Camil |
| author_facet | Belhadjoudja, Mohamed Camil |
| contents | This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by the characteristic flow of the time-invariant transport operator, transforming the original multidimensional system into a continuum of decoupled one-dimensional hyperbolic equations evolving along individual characteristic curves. A backstepping controller is then designed for each equation in the decomposition, and the resulting control laws are reassembled in the original coordinates to achieve finite-time stabilization of the full system. The framework relies on the existence of characteristic curves foliating the spatial domain, with uniformly bounded transit times (non-trapping). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25217 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Backstepping Control of First-Order Hyperbolic Equations in Arbitrary Dimensions with Non-Trapping Characteristics Belhadjoudja, Mohamed Camil Systems and Control Analysis of PDEs This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by the characteristic flow of the time-invariant transport operator, transforming the original multidimensional system into a continuum of decoupled one-dimensional hyperbolic equations evolving along individual characteristic curves. A backstepping controller is then designed for each equation in the decomposition, and the resulting control laws are reassembled in the original coordinates to achieve finite-time stabilization of the full system. The framework relies on the existence of characteristic curves foliating the spatial domain, with uniformly bounded transit times (non-trapping). |
| title | Backstepping Control of First-Order Hyperbolic Equations in Arbitrary Dimensions with Non-Trapping Characteristics |
| topic | Systems and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2605.25217 |