Submodularity of Energy Related Controllability Metrics
Abstract
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of actuators and sensors that optimize real-valued controllability and observability metrics of the network. We show that several classes of energy related metrics associated with the controllability Gramian in linear dynamical systems have a strong structural property, called submodularity. This property allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and for placement of power electronic actuators in a model of the European power grid.
Keywords
Cite
@article{arxiv.1403.6351,
title = {Submodularity of Energy Related Controllability Metrics},
author = {Fabrizio L. Cortesi and Tyler H. Summers and John Lygeros},
journal= {arXiv preprint arXiv:1403.6351},
year = {2016}
}
Comments
7 pages, 2 figures; submitted to the 2014 IEEE Conference on Decision and Control