On the Isospectral Nature of Minimum-Shear Covariance Control
Systems and Control
2026-04-10 v1 Systems and Control
Abstract
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.
Cite
@article{arxiv.2604.07608,
title = {On the Isospectral Nature of Minimum-Shear Covariance Control},
author = {Ralph Sabbagh and Asmaa Eldesoukey and Mahmoud Abdelgalil and Tryphon T. Georgiou},
journal= {arXiv preprint arXiv:2604.07608},
year = {2026}
}
Comments
5 pages, 1 figure