Isospectral steering characterizes reachable covariance sets for the differential Lyapunov equation when the gain matrix is constrained to fixed eigenvalues, using multilinear algebra and the Birkhoff-von Neumann theorem.
On the Isospectral Nature of Minimum-Shear Covariance Control
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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.
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Isospectral Steering
Isospectral steering characterizes reachable covariance sets for the differential Lyapunov equation when the gain matrix is constrained to fixed eigenvalues, using multilinear algebra and the Birkhoff-von Neumann theorem.