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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00225 |
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| _version_ | 1866917941157560320 |
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| author | Vazquez, Rafael |
| author_facet | Vazquez, Rafael |
| contents | This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary stabilization with finite-dimensional actuation by combining backstepping with Fourier analysis, deriving explicit necessary conditions. Second, for reaction-diffusion equations on sector domains, we use angular eigenfunction expansions to obtain kernel solutions in terms of modified Bessel functions. Finally, we outline a domain extension method for irregular domains, transforming the boundary control problem into an equivalent one on a target domain. This framework unifies and extends previous backstepping results, offering new tools for higher-dimensional domains where classical separation of variables is inapplicable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Backstepping Control Laws for Higher-Dimensional PDEs: Spatial Invariance and Domain Extension Methods Vazquez, Rafael Optimization and Control Systems and Control This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary stabilization with finite-dimensional actuation by combining backstepping with Fourier analysis, deriving explicit necessary conditions. Second, for reaction-diffusion equations on sector domains, we use angular eigenfunction expansions to obtain kernel solutions in terms of modified Bessel functions. Finally, we outline a domain extension method for irregular domains, transforming the boundary control problem into an equivalent one on a target domain. This framework unifies and extends previous backstepping results, offering new tools for higher-dimensional domains where classical separation of variables is inapplicable. |
| title | Backstepping Control Laws for Higher-Dimensional PDEs: Spatial Invariance and Domain Extension Methods |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2503.00225 |