NACO
On the pinning controllability of complex networks using perturbation theory of extreme singular values. application to synchronisation in power grids
Stéphane Chrétien Sébastien Darses Christophe Guyeux Paul Clarkson
Numerical Algebra, Control & Optimization 2017, 7(3): 289-299 doi: 10.3934/naco.2017019

Pinning control on complex dynamical networks has emerged as a very important topic in recent trends of control theory due to the extensive study of collective coupled behaviors and their role in physics, engineering and biology. In practice, real-world networks consist of a large number of vertices and one may only be able to perform a control on a fraction of them only. Controllability of such systems has been addressed in [17], where it was reformulated as a global asymptotic stability problem. The goal of this short note is to refine the analysis proposed in [17] using recent results in singular value perturbation theory.

keywords: Pinned control eigenvalue perturbation sum of rank one matrices singular value perturbation control theory
JIMO
A fast algorithm for the semi-definite relaxation of the state estimation problem in power grids
Stephane Chretien Paul Clarkson
Journal of Industrial & Management Optimization 2017, 13(5): 1-13 doi: 10.3934/jimo.2018161

State estimation in power grids is a crucial step for monitoring and control tasks. It was shown that the state estimation problem can be solved using a convex relaxation based on semi-definite programming. In the present paper, we propose a fast algorithm for solving this relaxation. Our approach uses the Bürer Monteiro factorisation is a special way that solves the problem on the sphere and and estimates the scale in a Gauss-Seidel fashion. Simulations results confirm the promising behavior of the method.

keywords: Power grids state estimation semi-definite relaxation Bürer Monteiro optimisation on manifolds

Year of publication

Related Authors

Related Keywords

[Back to Top]