On the Isospectral Nature of Minimum-Shear Covariance Control
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915926145761280 |
|---|---|
| author | Sabbagh, Ralph Eldesoukey, Asmaa Abdelgalil, Mahmoud Georgiou, Tryphon T. |
| author_facet | Sabbagh, Ralph Eldesoukey, Asmaa Abdelgalil, Mahmoud Georgiou, Tryphon T. |
| contents | We revisit Brockett's attention in the context of bilinear gradient flow of an ensemble, and explore an alternative formalism that aims to reduce shear by minimizing the conditioning number of the dynamics; equivalently, we minimize the range of the eigenvalues of the dynamics. Remarkably, the evolution is isospectral, and this property is inherited by the coupled nonlinear dynamics of the control problem from a Lax isospectral flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07608 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Isospectral Nature of Minimum-Shear Covariance Control Sabbagh, Ralph Eldesoukey, Asmaa Abdelgalil, Mahmoud Georgiou, Tryphon T. Systems and Control 93Cxx, 93C15, 49J15, 37J35, 93B05, 15A18 We revisit Brockett's attention in the context of bilinear gradient flow of an ensemble, and explore an alternative formalism that aims to reduce shear by minimizing the conditioning number of the dynamics; equivalently, we minimize the range of the eigenvalues of the dynamics. Remarkably, the evolution is isospectral, and this property is inherited by the coupled nonlinear dynamics of the control problem from a Lax isospectral flow. |
| title | On the Isospectral Nature of Minimum-Shear Covariance Control |
| topic | Systems and Control 93Cxx, 93C15, 49J15, 37J35, 93B05, 15A18 |
| url | https://arxiv.org/abs/2604.07608 |