Sparsity Preserving Discretization With Error Bounds
Abstract
Typically when designing distributed controllers it is assumed that the state-space model of the plant consists of sparse matrices. However, in the discrete-time setting, if one begins with a continuous-time model, the discretization process annihilates any sparsity in the model. In this work we propose a discretization procedure that maintains the sparsity of the continuous-time model. We show that this discretization out-performs a simple truncation method in terms of its ability to approximate the "ground truth" model. Leveraging results from numerical analysis we are also able to upper-bound the error between the dense discretization and our method. Furthermore, we show that in a robust control setting we can design a distributed controller on the approximate (sparse) model that stabilizes the dense ground truth model.
Cite
@article{arxiv.1903.11267,
title = {Sparsity Preserving Discretization With Error Bounds},
author = {James Anderson and Nikolai Matni and Yuxiao Chen},
journal= {arXiv preprint arXiv:1903.11267},
year = {2019}
}