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Sparsity Preserving Discretization With Error Bounds

Anderson, James and Matni, Nikolai and Chen, Yuxiao (2021) Sparsity Preserving Discretization With Error Bounds. IFAC-PapersOnLine, 53 (2). pp. 3204-3209. ISSN 2405-8963. doi:10.1016/j.ifacol.2020.12.1085. https://resolver.caltech.edu/CaltechAUTHORS:20210630-153134507

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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 be 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 model.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.ifacol.2020.12.1085DOIArticle
ORCID:
AuthorORCID
Anderson, James0000-0002-2832-8396
Matni, Nikolai0000-0003-4936-3921
Chen, Yuxiao0000-0001-5276-7156
Additional Information:© 2020 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0. Available online 14 April 2021. J. Anderson and Y. Chen are supported by PNNL on grant 424858. J. Anderson is additionally supported by ARPA-E through the GRID DATA program. N. Matni is supported in part by ONR awards N00014-17-1-2191 and N00014-18-1-2833 and the DARPA Assured Autonomy (FA8750-18-C-0101) and Lagrange (W911NF-16-1-0552) programs.
Funders:
Funding AgencyGrant Number
Battelle Memorial Institute424858
Advanced Research Projects Agency-Energy (ARPA-E)UNSPECIFIED
Office of Naval Research (ONR)N00014-17-1-2191
Office of Naval Research (ONR)00014-18-1-2833
Defense Advanced Research Projects Agency (DARPA)FA8750-18-C-0101
Army Research Office (ARO)W911NF-16-1-0552
Subject Keywords:Decentralized; distributed control; Discretization; Numerical methods
Issue or Number:2
DOI:10.1016/j.ifacol.2020.12.1085
Record Number:CaltechAUTHORS:20210630-153134507
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210630-153134507
Official Citation:James Anderson, Nikolai Matni, Yuxiao Chen, Sparsity Preserving Discretization With Error Bounds; IFAC-PapersOnLine, Volume 53, Issue 2, 2020, Pages 3204-3209, ISSN 2405-8963, https://doi.org/10.1016/j.ifacol.2020.12.1085. (https://www.sciencedirect.com/science/article/pii/S2405896320314609)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109669
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 Jul 2021 17:29
Last Modified:06 Jul 2021 22:02

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