Sparse Linear Ensemble Systems and Structural Controllability
Abstract
The paper introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern. Controllability of an ensemble system is, by convention, the capability of using a common control input to simultaneously steer every individual systems in it. A sparsity pattern is structurally controllable if it admits a controllable linear ensemble system. A main contribution of the paper is to provide a graphical condition that is necessary and sufficient for a sparsity pattern to be structurally controllable. Like other structural problems, the property of being structural controllable is monotone. We provide a complete characterization of minimal sparsity patterns as well.
Cite
@article{arxiv.2004.02783,
title = {Sparse Linear Ensemble Systems and Structural Controllability},
author = {Xudong Chen},
journal= {arXiv preprint arXiv:2004.02783},
year = {2021}
}