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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.05910 |
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| _version_ | 1866913139025510400 |
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| author | Yang, Shaohui Jones, Colin N. |
| author_facet | Yang, Shaohui Jones, Colin N. |
| contents | The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations with substantially lower construction errors and improved conditioning. A controllable linear system is first reduced to the staircase form via an orthogonal similarity transformation. We then derive a simple linear parametrization of the transformations yielding the unique Brunovsky form. Numerical stability is further enhanced by applying a deadbeat gain before computing system matrix powers and by optimizing the linear parameters to minimize condition numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerically Reliable Brunovsky Transformations Yang, Shaohui Jones, Colin N. Optimization and Control Systems and Control The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations with substantially lower construction errors and improved conditioning. A controllable linear system is first reduced to the staircase form via an orthogonal similarity transformation. We then derive a simple linear parametrization of the transformations yielding the unique Brunovsky form. Numerical stability is further enhanced by applying a deadbeat gain before computing system matrix powers and by optimizing the linear parameters to minimize condition numbers. |
| title | Numerically Reliable Brunovsky Transformations |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2512.05910 |