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
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

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