10 papers · 1 filter
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…
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…
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…
Automated algorithm design via Nevanlinna-Pick interpolation
Ibrahim K. Ozaslan, Tryphon T. Georgiou, Mihailo R. Jovanovic
The synthesis of optimization algorithms typically follows a design-first-analyze-later approach, which often obscures fundamental performance limitations and hinders the systemati…
Gradient Flows as Optimal Controlled Evolutions: From Rn to Wasserstein product spaces
Yongxin Chen, Tryphon Georgiou, Michele Pavon
We show that the continuous-time gradient descent in Rn can be viewed as an optimal controlled evolution for a suitable action functional; a similar result holds for stochastic gra…