15 papers
Isospectral Steering
Ralph Sabbagh, Tryphon T. Georgiou
We study the controllability of the differential Lyapunov equation under isospectral rotation of a linear gradient field. Specifically, control is effected by a symmetric time-vary…
On the Isospectral Nature of Minimum-Shear Covariance Control
Ralph Sabbagh, Asmaa Eldesoukey, Mahmoud Abdelgalil +1
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 conditioni…
The factorization of matrices into products of positive definite factors
Mahmoud Abdelgalil, Tryphon T. Georgiou
Positive-definite matrices materialize as state transition matrices of linear time-invariant gradient flows, and the composition of such materializes as the state transition after…
Tannenbaum's gain-margin optimization meets Polyak's heavy-ball algorithm
Wuwei Wu, Jie Chen, Mihailo R. JovanoviÄ +1
This paper highlights an apparent, yet relatively unknown link between algorithm design in optimization theory and controller synthesis in robust control. Specifically, quadratic o…
Minimizing Control Attention:The Linear Gauss-Markov paradigm
Ralph Sabbagh, Asmaa Eldesoukey, Mahmoud Abdelgalil +1
We revisit the concept of `attention' as a technical term to quantify the effort in calibrating control action based on available data. While Wiener, in his work on Cybernetics, an…
A lasso-alternative to Dijkstra's algorithm for identifying short paths in networks
Anqi Dong, Amirhossein Taghvaei, Tryphon T. Georgiou
We revisit the problem of finding the shortest path between two selected vertices of a graph and formulate this as an -regularized regression -- Least Absolute Shrinkage an…